I don't pretend to able to elucidate completely the Baptist position on baptism, even though I attended a Baptist church for 7 years and having only received infant baptism myself. I must also state that I could not have been more warmly received by the Baptist congregation I attended, in spite of our obvious differnces in this matter, nor could I think of a more Godly congregation of saints. But I understand that at the very least, they see baptism as a sign and a public declaration of one's faith in Jesus Christ after coming to faith in him.
Nor will I attempt to argue the issue at length. A couple of links
...explain things very nicely. That is not to say they will convince anyone holding the Baptist position, but they attempt to explain why those who baptize their infant children feel it is not an unreasonable postion.
What I would like to do is address the one passage often used as a proof text to by proponents of believer baptism, and just ask a few questions about it. The passage is Acts 2:38.
Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit.
I have had people take this verse to the point that Peter's words, "...repent and be baptized..." are to be understood as a chronological requirement for all time. You have heard the saying that a text without a context is a pretext. So let us ask the questions.
Q. To Whom was Peter speaking?
A. He was speaking to God-fearing Jews from every nation (Acts 2:5)
Q. When was he speaking?
A. He was speaking on the day of Pentecost, the first pentecost after Jesus' death and resurrection, and upon the occasion of the first ouptouring of the Holy S[pirit; what we now recognize as the birth of the Church.
Q. How many of his audience would previously have baptized in Jesus' name?
Q. Is it necessary, in light of the order in which Peter mentioned things, to be baptized before receiving the Holy Spirit?
A. No. Even Baptists would agree that one must have received the Holy Spirit before being baptized. No one can say, “Jesus is Lord,” except by the Holy Spirit. (1 Cor 12:3)
Q. Is it necessary, in light of the order in which Peter mentioned things, to repent before receiving the Holy Spirit?
A. No. In fact, it is the Holy Spirit who convicts of sin, so one cannot truly repent apart from the presence of the Holy Spirit. The Holy Spirit must come first.
Q. Had any of those who received the Holy Spirit that day, including the apostles themselves, been previously baptized in Jesus' name?
A. There is no evidence to indicate so.
In other words, it was a first on many levels; an occasion unprecedented and never to be repeated -- a one time occurrence. Now, we Christians would all agree that someone who has never been baptized, and who comes to faith in Christ, should indeed be baptized. And frankly, every one of Peter's audience would have been in that position on that day, so every one of them should have been baptized. But to take Peter's command in such a wooden, literal manner without really thinking it through; insisting on the chronology of repenting and being baptized, but ignoring that, in the passage, both precede the giving of the Holy Spirit, does it an injustice, and lays upon those who would be followers of Christ, a burden they do not need to bear. In short, it is a proof text that doesn't prove what they want it to.
PS: Just a couple of more things.
1. In the very next verse, (Acts 2:39) Peter tells his audience, an audience of adult men, that this is for their children as well. What did he mean? I just ask the question, even if my tongue somewhat in my cheek.
2. This is anecdotal only, but I have been told by a pastor friend who has been to the place in the Jordan River where John is said to have done his baptizing, that the river is so shallow that total immersion was most probably impossible. Christian groups do baptize there today, but apparently an area had to be dug out deep enough for the purpose.