Most baptist arguments are both commonly used, and very poor. They rely on people's ignorance of the Reformed position. John MacArthur's arguments here are representative, and taken from this article: http://www.gty.org/resources/sermons/80-369/is-infant-baptism-biblical#.Tp7nQpsUq30
I've tried to be succinct in my criticism, while providing effective refutations of these very common baptist arguments. John MacArthur's points are listed briefly as headings, and my answers are below. Thanks to a Lutheran (with whom I have strong disagreement), Charles Wiese for directing me to this article. Some of his arguments are also repeated here.
A Short Note on the Anabaptists
I have pointed out where possible the connection with the philosophies and the heritage of the Anabaptists at the time of the Reformation. This was a group which became infamous for being violent revolutionaries, hyper-spirituality, and even trying to set up a millenial kingdom of God on earth. An extreme example would be the city of Muenster which was taken in an Anabaptist rebellion. Jan Mattys, a self-styled prophet, called it “New Jerusalem.” His successor, John of Leiden, became notorious for polygamy and abuse of communism, before the city was captured and the rebels tortured and executed gruesomely. They were sometimes called the Radical Reformation, but not all the Anabaptists were as radical as this. Nevertheless, they formed a third separate group in distinction from the Reformers and the Romanists at the Reformation. They rejected Rome, and yet also claimed that the Reformers didn't go far enough. Today, this threefold distinction is still clearly seen, and readers must consider with which group they must be identified, to be in communion with the true church of the past.
Their commonly held views included refusing to submit to civil government in favour of setting up an alternative theocracy via rebellion (or alternatively, strict pacifism), refusing to take oaths, communion of goods, denial of personal property, direct revelations via prophecy, a future millenial kingdom, and of course, re-baptising converts to their religion. They did this because they judged the baptism of other churches as false and worthless. For these reasons, they were greatly persecuted as a dangerous, violent, and divisive sect. Many Baptists today deny their connection with these more radical groups, but really it is the theological heritage of their position, and their philosophy is closer, especially among Pentecostals (who are almost without exception Baptists), than they would like to admit.
Introduction: Infant Baptism Was Introduced in the Fourth Century
This was the same claim made by the Anabaptists. It's wrong. Today, many baptist groups are still trying to rewrite history to support their position, even trying to paint a rosier picture of the Anabaptist movement. Actually the historical defence is so painfully absent for the Anabaptist position that many resorted to a theology of restorationism. In contrast to successionism (the idea that there were always those who denied infant baptism), this view is that the gates of hell did actually prevail against the church for many years until God restored the church through the super-spiritual Anabaptists. This is much like the Mormon view of church history invented by Joseph Smith who claimed to be an apostle. MacArthur later concedes further to say that infant baptism "started appearing in the second and third century." While this view of church history could be effectively shown as totally false, the authority is Holy Scripture, not differing views of history.
1. Infant Baptism Is Not in Scripture
The Lord's Supper being administered to women is not in Scripture either, yet we all practice this. This shows that it is indeed legitimate to study scriptural principles by which it can be deduced. The baptists cannot fault us for doing this to prove infant baptism. We do not need to give baptists one single verse that proves it. This is a wrong view of Scripture and logic. This kind of argument, which downplays the use of deduction by “good and necessary consequence,” was the same philosophy of the Anabaptists. The baptist confession that is closest to the Reformed faith, is the London Baptist Confession of 1689 (LBCF) which is mostly the same as the Westminster Confession (WCF) of the Presbyterians. In WCF 1:6, the authority of that which “by good and necessary consequence may be deduced from Scripture” is asserted. This statement is absent from the LBCF!
a. The Reformers Didn't Jettison Infant Baptism out of Fear of Persecution
Baptists claim the Reformers didn't go far enough because they were afraid of Rome. Unless they can answer the following question, they need to drop this argument. Why would they compromise on this issue, when justification by faith alone was already more than enough to have them burnt?
b. Matthew 19:14, Mark 10:14, and Luke 18:16 Only Mean That God Has a Special Care for Children.
Luke says specifically that infants were carried by their parents, and that Christ blessed them. If Christ blesses someone, and all authority on heaven and earth belongs to him, surely they cannot be cursed, and are therefore saved. He also told his disciples, “of such is the kingdom of heaven.” If these infants brought to Christ are actually citizens of the kingdom of heaven, how can we refuse them baptism? One cannot be a citizen of this spiritual kingdom and not be a member of the church. Therefore citizenship in the kingdom, just as much as membership in the church, is symbolised in baptism.
What does "a special care for children" even mean? If anything, Baptist theology teaches that God has a special care for adults. Besides, if all children were equally precious to God, how does he explain the slaughter of the Canaanite men, women, and children, the slaughter of the Amalekites, or the dashing of Babylon's little ones against the rocks in Psalm 137?
c. All members of the households that were baptised all believed first.
Yet before Paul even met the Philippian jailor's household, he told him, "Believe and thou shalt be saved, and thy house." Surely this meant that if he believed, his household would also be saved? We know it did not necessarily mean that there will be no reprobates in his house, as Rom. 9:6-8 explains. Scripture simply doesn't say that they all believed first in any of the examples of household baptisms. Nor does it ever say there were no infants. This is unlikely notion is forced on into the text by baptists. Admittedly it doesn't say explicitly that there were, which is why we would prefer to use stronger arguments. Even so, the only examples of specific baptisms in which households were not also baptised, are Christ, the eunuch who was a eunuch, and Paul who was single.
2. Infant Baptism Is Not New Testament Baptism.
This would mean that all Reformed and Presbyterian churches are full of people who have never been baptised. This position is not simply baptist, it is Anabaptist, because it means we all need to be re-baptised.
a. Baptise Means Immerse.
What about I Cor. 10:1-2? Who was immersed at the Red Sea, the children of Israel (which definitely included infants!), or wicked Pharoah and his armies? What would “immersed unto Moses” even mean? Many more examples could be given which demonstrate a use of “baptise” which cannot mean “immerse.” Consider also why the translators went to the trouble of inventing a new English word “baptise,” if using the word immerse would have been sufficient. We hold that to baptise something indicates a change being made to something by means of contact with something else. Most generally the idea of washing seems to be intended, as being a very basic change from dirty to clean by use of water. The word has also been used to describe dyeing clothes a different colour, a person becoming drunk with wine, or in the example above, the children of Israel all taught under the ministry of Moses.
b. Baptism Is a Picture of Union With Christ in His Death, Burial and Resurrection.
How does submerging symbolise Christ's death of being nailed to the cross? How does full immersion symbolise Christ's burial in a tomb above ground by a stone rolled in front of the cave? How does emersion (lifted out of the water) symbolise Christ's resurrection? The picture ought fit the reality. And if baptism means immersion, how can emersion be part of the symbolism and their practice? And even if it was meant to symbolise modern burial practices, why use water instead of soil, dirt, and earth? In the baptist picture, there's no logical basis for using water. Their error comes from thinking that Romans 6 is speaking about the sacrament. It's not. Even so, it doesn't speak about immersion. It's speaking about the further implications of the reality of being united to Christ which it calls baptism in Christ, and describes as being “planted.” If it was speaking about the mode of the sacrament, then planting would be appropriate picture.
Baptism is union with Christ; spiritual baptism, not water baptism. There is no water in Romans 6. Water baptism pictures spiritual baptism; the washing of regeneration which saves us (I Peter 3:20-21; Titus 3:5). By this we are united to Christ, and therefore united also in His life, suffering, death, burial, resurrection, and even with His session at the right hand of God in heaven (Eph. 2:6). Since it symbolises spiritual washing from sin, water used for washing is most appropriate. And since Scripture speaks of this reality never as immersion, but as being sprinkled with the blood of Christ, and having the Holy Spirit poured on us, then sprinkling or pouring are the most appropriate methods.
Baptism is union with Christ; spiritual baptism, not water baptism. There is no water in Romans 6. Water baptism pictures spiritual baptism; the washing of regeneration which saves us (I Peter 3:20-21; Titus 3:5). By this we are united to Christ, and therefore united also in His life, suffering, death, burial, resurrection, and even with His session at the right hand of God in heaven (Eph. 2:6). Since it symbolises spiritual washing from sin, water used for washing is most appropriate. And since Scripture speaks of this reality never as immersion, but as being sprinkled with the blood of Christ, and having the Holy Spirit poured on us, then sprinkling or pouring are the most appropriate methods.
c. Infants Can't Have Faith.
Instead of considering Scripture, the baptists resort to rationalism, scoffing at the very idea of infants having faith. Yet Scripture even speaks of infants not only having faith, but exercising it! Consider John the Baptist who leaps for joy in the presence of Christ (Luke 1:15, 41, 44), Jeremiah who was sanctified before birth (Jer. 1:5), David who was made to hope when a suckling (Psalm 22:9), or even Christ. These are not unique examples; God is indeed praised by babes and sucklings (Psalm 8:2), and Christ refers to this in order to rebuke the Pharisees for complaining at the praise of young children (Matt. 21:16).
3. Infant Baptism Is Not a Replacement for Circumcision.
In contrast, Colossians 2:11-12 identifies baptism with circumcision.
a. Circumcision Was Just a Sign of Ethnic Identity.
Romans 4:11 calls circumcision a sign and seal of the righteousness of faith. Isn't this also what the sign of baptism is? Yet, John MacArthur claims that circumcision has nothing to do with symbolising salvation. He is a dispensationalist who believes (like many Anabaptist did), in a future millenial kingdom, specifically for the ethnic Jews. If it does mean ethnic identity in addition, this means the circumcised are to be counted as the children of Abraham. In fact, one cannot be counted as a child of Abraham without the sign of the covenant. Remember that this is an everlasting covenant (Gen. 17:7-11). We see in the New Testament that Abraham is called the father of the faithful (Rom. 4:11-14). Gentile Christians are called true Jews (Rom. 2:27-28), and children of Abraham (Gal. 3:7).
This is explained to mean that through faith, not through the law, we are the recipients of all the promises and blessings of God in Christ, Abraham's seed (Gal. 3:8-29). The gospel of the justification of the heathen was preached to Abraham when he was told that all nations would be blessed through him. It is through faith in the promise that we receive the inheritance promised to Abraham and his seed, because the covenant of God is everlasting and unconditional, and therefore cannot be disannulled. This is because the covenant is with Christ, the promised seed of Abraham, who is also the only Mediator of the covenant, and we, with Abraham and all who believe, are in Him. Notice also, that this means we are the proper recipients of the inheritance promised to Abraham, described to him as the land of Canaan to given as an “everlasting possession.” Romans 4:13 explains that this meant that Abraham, with us, would be heir of the world. Since baptism signifies then that we are Christians through faith, that is, the true children of Abraham, it has exactly the same meaning and function as circumcision did. And if circumcision could legitimately be applied to children (indeed it had to be!), then baptism can be too. In fact, when one considers that it is the sign of the covenant with us and our children, it must be!
b. People Believe Infant Baptism Saves Them
Many have wrong superstitions about the Lord's Supper too. The consistent Reformed view is that just like the preaching, the sacraments are only of benefit to the elect through faith.
c. Presumptive Regeneration and the Federal Vision Are Wrong.
MacArthur is right to condemn this false doctrines. Nevertheless, God does promise to save our children, not head-for-head, but according to the election of grace (Rom. 9:6-8). Therefore, just as Scripture teaches, we believe in the promised salvation of our children (and therefore promised regeneration, not presumed), even though we also believe and bear in mind that there may be reprobate children of the flesh too. And we believe this not because we have baptised our children, but we baptise them because of this covenant promise of God. The promise of salvation is given just as much to adult believers as to their children (Acts 2:39), though we know that there may be reprobates among the children of the flesh, just as much as there may be hypocrites among the adults. The promise is to the elect, whom God draws unto Himself.
Yet, we cannot differentiate between the wheat and tares (Matt. 13:29). In time the reprobate may manifest themselves by their wickedness, and be put under discipline and eventually excommunicated, yet others remain hidden hypocrites, and still others who are elect may be excommunicated and later brought to repentance (I Cor. 5:1-8; II Cor. 2:6-8). This doesn't make us lazy in bringing up our children in the nurture and admonition of the Lord (Eph. 6:4), but rather gives us confidence that it's not all in vain!
4. Infant Baptism Destroys the Nature of the Church.
Another old Anabaptist belief was the idea of a pure church with only regenerate membership. This also shows that they really exclude in every sense their children from the church and kingdom of Christ, since they deny that an infant can be regenerate. But Christ said, "of such is the kingdom of God," and, "Forbid them not to come unto me" (Mark 10:14). He was not simply referring to the infants who were not even able to come of themselves, but to the parents who had to carry the babes in their arms! This false belief about the church also means that Reformed and Presbyterian churches are not true churches at all.
Their inconsistency is that baptised adults can be unregenerate, hypocrites, and apostatise, just as much as those who were baptised as infants. Their idea of the reality of a regenerate church is never a reality. In a great house, there are vessels present for different purposes; some noble, others ignoble (II Tim. 2:18-20). There are always tares among the wheat. While the Reformed recognise that God has a purpose with hidden tares in the church, the baptists try to root out the tares and in doing so root out the wheat (Matt. 13:29, 38). The Reformed recognise that the goal of church discipline is not to rigorously try to root out all the reprobate, but to seek the holiness of each member. The baptist will point out that Christ said that “the field is the world,” as if this meant that the tares in the world are not also present in the church. Since the wheat is also in the world, we cannot imagine that Christ meant that there are no tares in the church. This would completely overturn his presentation of the tares being mixed among the wheat, and the difficulty in discerning the difference between the two until harvest time. The church most certainly is in the world (but not of the world; John 17:11, 14-16), and therefore the tares sown in the world will be found in the church also. This is the reality in baptist churches too. If Christ commands the very angels not to try to uproot the tares before the final judgment, in case they uproot the wheat, how much more should the baptists heed this command?
Historically the Anabaptists have been guilty of world-flight, thinking that the key to holiness lies in a physical, even geographical separation of the church from the world. Even if it were possible to flee the reprobate entirely, we still bring the wicked world with us in our old sinful nature. Instead God has a purpose with close contact of the elect and reprobate, even placing reprobate children, like Esau, in covenant homes, amidst elect children. God wills for them to be hardened in the church, and for the elect to be tested by them for their sanctification. We could deduce many more reasons also.
5. Infant Baptism Is Not Consistent With Reformed Soteriology
This claim is very short-sighted. Doesn't the sprinkling of water on a helpless baby who does nothing far better illustrate that God is the one alone who saves us by the sprinkling of the blood and Spirit of Christ, entirely of grace, according to His unconditional election, before we have done any works whatsoever? Since the Reformed believe in infant salvation, it would be totally inappropriate if we did not baptise infants. The baptist complains that not all the babies are saved. Yet Isaac was commanded to circumcise reprobate Esau even though he would not be saved, as a sign of God's everlasting covenant with us and our elect children. Not all baptised adults are saved either. Does this nullify the symbolism of baptism, and its benefit to the elect through faith? And how can the claim be made that God has a special care for children when the claim is also made that they are not regenerate, not members of the church, and cannot have faith!
While the baptism of infants illustrates the sovereignty of God in salvation, as well as the covenant of God maintained from generation to generation, the baptist practice does not correctly symbolise the work of regeneration, or God's sovereignty in it, and certainly doesn't show anything about God's covenant with us and our children. The focus in immersion is entirely on the person going under and coming up, doing all the action, while the water does nothing. It is actually re-baptism that nullifies what baptism is supposed to signify. I grant that from their faulty perspective, this is not what they think they are doing, but if infant baptism is valid (as we have seen), then they are actually re-baptising.