If one assumes that Mathew 16: 16 - 20 establishes Peter as the head of the church, then one must also assume that Mathew 16: 21 - 23 establishes Peter as Satan. You can’t cherry pick the scriptures.
I am of the opinion that NEITHER assumption is true. That both are figurative and not to be taken literally. Further, the “rock” or foundation that Jesus is referring to in 16 - 20 is “Thou art the Christ, the Son of the living God”.
Just like in verses 21 - 23, Jesus is pointing out that Peter’s outburst is not according to God’s will. And since it is not in alignment with God’s will, it was inspired by Satan.
Works for me.