Who is Jesus? It's a very valid question that needs a solid answer. I love looking at the responses: John the Baptist, Elijah, Jeremiah or one of the prophets. These responses are not coming from the people that were against Jesus. His enemies thought He was or had a demon. This uncertainty about who He was was coming from His followers.
He had been gradually revealing the truth about who He really was throughout the gospels. He was the Messiah the whole time, but His followers didn't fully recognize it at first, and He gave them time to gradually come to that understanding. Now it was time for a definitive statement, and it came from Peter: "You are the Christ, the Son of the living God."
There are likely reasons that Peter was the one that spoke. It's clear that he was often the spokesperson, and it may be for as simple a reason as he was the oldest of the disciples. Peter came to this conclusion through his observations of Jesus, probably through his knowledge of the Torah, and through gradually deepening understanding of these things. That is to say, these are the things that prepared his heart for greater understanding. Because only God, in granting him the light of faith, could allow him to see the truth of the statement that he was able to make.
I'd be willing to bet that Peter was not the only one that had come to realize this. It was probably bouncing around in the heads of some of the other disciples as well. Some may have already come to believe it, and others may have just started to ask themselves "Could it be?" But Peter was the one to answer.
I think that it's interesting that this is how the papacy and the magisterium often works. When a subject comes up for whatever reason, there are a lot of people throwing out different ideas about a topic. Many of the ideas have merit, but what's the definitive answer? That's where we turn to the pope for answers. Keep in mind that the pope is not necessarily the only one that has reached this answer, but he is the one that has been given the authority to answer the question in a way that we can all listen to with confidence. Also keep in mind that he didn't make up the answer. He may have spent a lot of time in study and prayer to reach the answer, and ultimately it is God that helps him to understand the answer.
I guess that's just verses 13-17. I think this is going to have to extend to pope post #4 for the next few verses. I'm not sure how long this is going to go on; because this still isn't the post that I really wanted to write! I keep getting sidetracked. How does that happen?