What’s interesting from the story as recorded in the gospel of Mark is it does not mention the reply of Jesus to Peter for his confession: “And I tell you that you are Peter, and on this rock I will build my church, and the gates of Hades will not overcome it.” (Mat 16.18) This sentence has of course been used by the Roman church to justify the primacy of Peter (and, somewhat correspondingly, the bishops of Rome who succeeded Peter). Perhaps Mark didn’t include it because it was written in Rome anyway (if we trust the prevailing tradition) where the primacy of Peter was assumed and thus did not need any explicit justification. To construe the problem from a different perspective, what would be interesting is to ask why Matthew added Jesus’ reply to Peter for his story. The simplicity of Peter’s confession in Mark and its more complex variant in Matthew (and Luke, for that matter) also supports the hypothesis for the priority of Mark in the Synoptic problem. It does not always work this way, but it does for this case.
Jesus then warned his disciples not to tell anyone that he was the Messiah, presumably because the disciples would understand Jesus’ Messiahship in a purely political manner, such that if they start telling everybody that Jesus was the Messiah, it could mean a call to insurrection to overthrow the Herodian dynasty and Roman occupation. Indeed, that’s why Jesus immediately said that the mark of his Messiahship is suffering and rejection, which does not make any sense at that time — and now. No rebels in Libya will claim that they will save the country by going to Tripoli to be massacred by Gaddafi.
Interestingly, the story was immediately followed by the story of transfiguration in all Synoptics, where Jesus was glorified in a high mountain. The voice from above confirmed what Peter had said previously from below. Jesus is indeed the Son of God, a title which also has a Messianic connotation, although no doubt the church would read it multidimensionally — and now they (Jesus and his disciples) would inevitably proceed to Jerusalem, where he was fated to clash against the arch-nemesis of God and to win the battle with suffering and crucifixion.