Matthew 16:13-20 is controversial. Was Peter called the rock on which the Church was built? It is unclear. Jesus most likely spoke in Aramaic and used the word Kepha for rock. The choice of two Greek words Petra and Petros were grammatical and do not necessarily make it clearer. In the Old Testament God is called the Rock of Israel. The rock of Daniel’s prophecy which conquered Rome was Christ. We don’t establish doctrine on unclear passages. What did Peter say? He said that another rock, Christ was the cornerstone (1 Peter 2:7-8), a rock (Petra) that makes men stumble. Peter was the first to proclaim this faith, but in his letters Peter merely introduced himself as an Apostle, not chief Apostle. To claim that Peter was the first Pope reads more into the passage than it says.
reference: The Matthew 16 Controversy