Dan (my Presbyterian friend) and I have been recently discussing the issue of infant baptism and he has posted our arguments for and against it on his website. You can read them here:
I’ll also let Mark Dever, a Baptist, weigh in on this discussion with his brief summary of five reasons against infant baptism:
1) Nobody disagrees with believer baptism. The debated point is infant baptism.
2) There are no clear examples in the New Testament of infant baptism.
3) There is no clear teaching on infant baptism in the New Testament.
4) The New Testament nowhere teaches a parallel of physical circumcision with physical baptism. In fact, Colossians 2 exactly parallels spiritual circumcision with physical baptism, that is, the circumcision of the heart with physical baptism. This would support the idea of baptizing only those who give evidence of being born again.
5) Historically, infant baptism is not in the New Testament, and it is not in the Didache, and early second-century manual of Christian worship. There is no certain record of it in the first century, or even in the second century. In the third century, there is certain record of infant baptism, but it is not the infant baptism which some of our Reformed Protestant friends teach. It is rather what the Roman Catholic church now teaches-that baptism actually effects our being born again, our regeneration, our salvation. The idea of infant baptism that some of our reformed Protestant friends teach, in fact, does not appear until after other Protestants in the 1520’s have re-introduced the practice of believer baptism. It is really Huldrich Zwingli who pioneers the idea of an infant baptism that is not salvific or regenerating.
(From A Display of God’s Glory 2nd ed., pg. 52)