“Peter”, Strong’s # 4074, is the Gr. PETROS, a “rock or a stone” is the name Jesus gave to Simon the fisherman. This “rock” is not the same as the Gr. PETRA, a “large stone”, “crag”, “projecting rock” which Jesus declared His church would be built upon. Jesus play on names would sound like this to us: “And you are Stone, and upon your Boulder of a Confession that I’m the Christ of God, I will build my Church” Mt 16:16-18.
The church of Christ was not built upon the Stone Peter, but it is built upon the Christ who is the foundation and cornerstone. “The Stone which the builders rejected became the chief cornerstone” 1 Pt 2:7. And, “For no man can lay a foundation other than the one which is laid, which is Jesus Christ” 1 Cor 3:11. There is ample evidence that the church of Christ is built upon the person Jesus Christ.
There is no evidence that it is built upon Peter. Peter was a significant Apostle, but Peter had no higher position than any other Apostle. The objection says, “But Jesus gave the keys of the kingdom to Peter.” The response is, “Not any more than He gave to the other Apostles. Compare the two passages in Matthew:
To Peter – Mt 16:19: 19 “I will give you the keys of the kingdom of heaven; and whatever you bind on earth shall have been bound in heaven, and whatever you loose on earth shall have been loosed in heaven.”
To the the Church – Mt 18:18 18 “Truly I say to you, whatever you bind on earth shall have been bound in heaven; and whatever you loose on earth shall have been loosed in heaven.”
In both instances, His kingdom/church are given authority to bind and loose sins. To open and close. The spiritual agents of God like Peter, the Apostles, and church members are doing God’s will on earth to build and protect the kingdom/church. The authority Peter had in the first century to “bind” or “loose” sins is not changed today. The church of Christ must exercise the same authority today that the kingdom not be harmed.
Jesus called Peter, PETROS, but Jesus built His church on PETRA, the Gibraltar stone of a confession that Jesus is the Christ, the Son of God.
This is important for us as Christians to recognize. No doubt Peter played an important role in the foundation of the Church. Peter was chosen by the Lord to deliver the first gospel sermon. But as you pointed out Peter himself he recognizes Christ as the true foundation of the Church. We (the church) are like Peter. Living stones being placed on the foundation of Christ. Very encouraging.