Because his Lord had commanded him to baptize people as part of making disciples and bringing them into the church.
Nothing our Lord commands is in vain.
Peter did not change his theology, but perhaps the way many understand it is not precisely like he understood it.
Three times in the early part of Acts, Luke records Peter preaching to a group of people in which he mentions receiving the forgiveness of sins (
Acts 2.38; 3.19-21; 5.31.32), and in two of the three, he only mentions repentance but not baptism. Joined to this, in
Luke 24.46-49, Luke records Jesus's final instructions on what Peter and the other apostles are to preach. Jesus mentions repentance and the forgiveness of sins, but not baptism. If we read Luke and Acts as Luke intended (back to back as two parts of one history), we see that within just a few pages he includes four passages that are clearly parallel in content, and in three out of four, forgiveness and repentance are mentioned, but not baptism.
Interestingly there is a variant reading at
Luke 24.47, and some of the oldest manuscripts read "repentance for the forgiveness of sins.")
In light of this evidence and later how Peter says that the proof Cornelius and the other Gentiles had been cleansed by faith was they had received the Spirit, I would suggest that repentant faith and baptism do not play the same role in someone receiving the remission of sins. Repentance and faith seem indispensable in a way that baptism is not. In those parallel passages to
Acts 2.38, what is absolutely essential to bringing about the remission of sins, repentance, is mentioned while what is not, baptism, is not.
This is not to suggest that baptism is optional. Even though baptism was not the place where Cornelius was forgiven, Peter still commanded him to be baptized. Baptism is commanded for all, and so all must be baptized. No one can reject baptism and be saved.
Under normal circumstances in the Book of Acts, forgiveness/remission did, in fact, come to someone by faith and repentance at baptism--not because baptism had effected the remission of sins but because it was the usual setting in which the repentance and faith that did effect it was expressed. When someone said they believed the gospel, the church at once led them to baptism. Cornelius's situation, however, was not normal circumstances. At that point, the church would not have baptized him and other Gentiles. God had to do something extraordinary and prove he had accepted them, and in doing this, it was revealed that it is possible in certain circumstances for God to bring someone to faith and repentance before baptism and so remit their sins and cleanse them before baptism. This is definitely not the pattern in Acts, though.
It is, however, certainly common now. In the circumstance when someone is led by the church to receive the Spirit before baptism (which is something that the church in Acts never led someone to do), that person must be commanded to be baptized, and if they truly have saving faith they will. I would even say in order for them to maintain their forgiveness--their cleansing received before baptism--they must be baptized.
Peter was not trying to hide anything. He focused on what strengthened his argument in that context.
I think the drive to include their entire experience in their cleansing is not rooted in carefully interpreting this passage but in bringing to it a pre-commitment to the idea that only baptism can bring about the forgiveness/remission of sins.
I know we disagree, but I appreciate the discussion and your questions that challenge me to think through my beliefs again.