Jesus renamed Simon as Rock Jesus using words paralleling Isaiah 22, which every Jew of the time should have recognized. Then Jesus gave the keys of the kingdom to Rock (Peter) and to no other Apostle.
In Isaiah, the keys to the kingdom are given to the prime minister by the king so that the people know the prime minister has full authority when the king is absent.
What did Paul say about the position of Peter?
Ga. 2:9 James, Peter John, those reputed to be pillars, gave me and Barnabas the
right hand of fellowship when they recognised the grace
given to me. They agreed that we should go to the Gentiles,
and they to the Jews.
Ga. 2:10 All they asked was that we should continue to remember the
poor, the very thing I was eager to do.
Ga. 2:11 When Peter came to Antioch, I opposed him to his face,
because he was clearly in the wrong.
Ga. 2:12 Before certain men came from James, he used to eat with the
Gentiles. But when they arrived, he began to draw back and
separate himself from the Gentiles because he was afraid of
those who belonged to the circumcision group.
Ga. 2:13 The other Jews joined him in his hypocrisy, so that by their
hypocrisy even Barnabas was led astray.
Ga. 2:14 When I saw that they were not acting in line with the truth of
the gospel, I said to Peter in front of them all, “You are a
Jew, yet you live like a Gentile and not like a Jew. How is it,
then, that you force Gentiles to follow Jewish customs?
Galatians 2:9-14 NIV
Paul does not treat Peter as the Overlord of the Christian Church. In this passage in Galatians, Paul says that Peter is one of several men who are “reputed to be pillars” of the Church. He does not see himself as taking orders from the Pillars or from any one of them.
In Galatians 2:11, Paul flatly opposes Peter. Paul believes that Peter is acting like a hypocrite and being too soft on Judaizers. Paul doesn’t treat Peter as the Chief Apostle. He doesn’t treat Peter as the symbolic head or the organizational head of the Christian Church.