I disagree. Peter was never seen in Scripture as the Leader of the entire Church. Shortly afterward, Jesus is rebuking Peter and saying "Get thee behind me Satan!" Paul rebukes him as well. Regardless of the rebukes, Peter is nevertheless NEVER seen as THE head of Christ's church on earth. A leader, yes. THE leader, no. And since Scripture was written into the 90s, and the book of Acts covers the ACTS OF THE APOSTLES, that's a pretty significant omission.
The Rock was Peter's bold confession about Jesus. It's the truth that HE, Jesus, is the Messiah. Upon that truth he will build His church. Peter was called a rock because of his boldness, steadfastness, and unyielding spirit to confess something that could have gotten him stoned. Peter knew the truth. If fact, he knew who the TRUTH was. And Jesus was pleased. He did not make him (Peter) the governor over all the church. In fact, in the broader context, Jesus gave the Keys to the church itself (as is seen just two short chapters later), not Peter exclusively.
A leader, yes. THE leader, no
The Keys and the Feed my Sheep episode appoint the single leader, and it is indicated by his leadership in winning the first converts, leading in the issue of dietetic law, and several miracles described in Acts. St John Chrysostom called Peter Prince of the Apostles. It is true that St, Paul lists also St. James and St. John as "pillars".
The Rock was Peter's bold confession about Jesus
This is your opinion? The renaming indicates a personal attribute of Simon bar Jonas. You can spin it that way, -- I have no serious objection to it, as indeed his confession prompted the renaming and the keys episode, but it is your commentary, nothing more.
Jesus gave the Keys to the church itself (as is seen just two short chapters later), not Peter exclusively
This is not accurate scripturally. The Apostles are given the power to bind and loose in the context of the teaching authority of the Church, but the keys are not given them.