Also the Matthew passage says, to paraphrase, "You are Peter the Rock and on you I will build my church…etc. It does not say, “Peter you are the first of a long line of successors who rule be the head of my church, speak infallibly, create one approved liturgical system.”
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Let me try to address this in this way…the tradition of that time and culture.
Consider the name change. Peter was the only one of the Apostles whose name was changed…and you can see Jesus saying this the first time they meet…in John 1:42…42 He brought him to Jesus. Jesus looked at him and said, “You are Simon the son of [a]John; you shall be called Cephas” (which is translated **Peter).
Christ was not given to meaningless gestures, and neither were the Jews as a whole when it came to names. Giving a new name meant that the status and authority of the person was changed…this was the culture and understanding of that time.
Consider the following significant name changes in the Bible and commands that followed the name change:
Abram to Abraham……Gen 17:15….Neither shall thy name be called any more Abram: but thou shalt be called Abraham: because I have made thee a father of many nations.
Jacob to Israel….Gen 35……. 10And God said unto him, Thy name is Jacob: thy name shall not be called any more Jacob, but Israel shall be thy name: and he called his name Israel………. 11And God said unto him, I am God Almighty: be fruitful and multiply; a nation and a company of nations shall be of thee, and kings shall come out of thy loins;
Simon to Cephas/Peter…Matt 16…17 Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven. 18 And I tell you that you are Peter,** and on this rock I will build my church, and the gates of Hades[c] will not overcome it. 19 I will give you the keys of the kingdom of heaven; whatever you bind on earth will be[d] bound in heaven, and whatever you loose on earth will be[e] loosed in heaven.”****