There are different interpretations of Christ's words, as you know. The typical Protestant interpretation of Jesus reference to "upon this rock I will build my church," is to Peter's confession of Jesus as the Christ, the Son of the Living God, not to Peter himself. It is upon that confession that Christ's church would be built, not upon the man Peter. And the history of the early church bears this out. It was Paul, not Peter, who planted the churches throughout Asia Minor. It was Paul's teaching that caused those churches to grow, not Peter's. Anyone who acknowledges and puts their faith in both the person and the work of Jesus ("the Christ, the Son of the Living God" -- similar to Peter's confession) will be saved, are placed in spiritual union with Him, and become part of His church.
From church history, this interpretation makes the most sense.
It was Paul, not Peter, who planted the churches throughout Asia Minor. It was Paul's teaching that caused those churches to grow, not Peter's. But note something very important. While Paul founded many churches, it was the churches that Peter founded which were the most important and authoritative "patriarchal" churches: Antioch and Rome (and even Alexandria, through Peter's disciple Mark). These Churches exercised a special primacy in their respective regions and went on to become the recognized seats of the three original Patriarchates.
Paul's churches had no such special patriarchal authority.