Peter has the keys; that is, Peter understand and can convey what kingdom life is like, what kingdom residents are like.
Jesus built this church and entrusted Peter with it.
(with thanks once again to Boring & Craddock's The People's New Testament Commentary)
Jesus had called himself the Son of Man (verse 13), but Peter called him the Son of the living God (16). I'm saving discussion of "Son of Man" for another time, and right now looking at the "Son of God" designation. Since Jesus is the Son of God, then God is his father. Jesus assents to this relationship when he says "....my Father in heaven." I've been reading Julian Sheffield's essay, "The Father in the Gospel of Matthew," in A Feminist Companion to Matthew, edited by Amy-Jill Levine:
The term, father, is used for God 65 times in the synoptic gospels (Matthew, Mark, and Luke). 44 of those are in Matthew. God the father is identified as "heavenly" or "in heaven" 20 times in Matthew.
Sheffield instructs us that this interpretation of God as heavenly father comes from the context of Rabbinic prayer language. This language emphasizes who is in charge--God, not Caesar.