I find the literalism of the disciples entertaining. Jesus wrangles them into understanding that he's talking about teaching of the Pharisees, not actual bread. If creating understanding was that much work why not just say, "Beware of the Pharisees' teaching?"
Jesus' immediate reaction to Peter's confession, "You are the Christ, the Son of the living God," tells us the source of faith: "Flesh and blood has not revealed this to you, but my father in heaven." Comprehending who Jesus is requires supernatural intervention. You cannot 'get' Jesus apart from God's grace.
Two things happen once he is identified as the Messiah. He tells them not to tell. He couldn't deal with a lot of messiah-talk. And, he starts to tell them about Jerusalem. They do not like the Jerusalem-talk, either.