This idea comes from a misunderstanding of Matthew 16:17-18 . To understand this passage correctly we need to consider two statements made by the apostle Paul about the foundation of the church. First, he declared that the body of Christ is “built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief cornerstone” ( Ephesians 2:20 ). In these verses Paul clearly portrayed Jesus Christ as the cornerstone, and the apostles and prophets as foundation stones fitted around and upon Him. Second, in 1 Corinthians 3:10-11 Paul referred to himself as a builder erecting a superstructure on Jesus Christ, who is the foundation of the church. Neither of these passages indicates that Peter is the foundation of the church. As one of the apostles, he is included, but he receives no special recognition.
There is an interesting play on words hidden in the Greek text of Matthew 16:18 . Jesus said, “I also say to you that you are Peter”(Greek petros). Literally, we would read this, “You are Rock.” Then our Lord added, “And on this rock (petra) I will build My church.” The Greek word petra refers to a huge boulder or rocky cliff rather than a stone. He didn’t say He would build the church on Peter, but on “this rock,” the truth Peter had so nobly confessed when he said, “You are the Christ, the Son of the living God” ( Matthew 16:16 ). In other words, Jesus was indicating that the church would be built on Himself. He alone is the Rock, the Cornerstone.
Some scholars object to this interpretation because they say that Jesus probably spoke in Aramaic, a language that doesn’t have this distinction between a masculine and feminine form of the word rock. This argument is beside the point. Jesus could easily have made the same distinction through the inflection of His voice or a gesture. The significant fact is that the inspired author (Matthew) used two different Greek terms. If Jesus wanted to tell Peter that he was the rock upon which the church would be built, He could have said it very clearly. He could have said, “I tell you that you are Peter (petros ), and on you I will build My church.”
The idea that Jesus appointed Peter as the first pope is not supported in this verse or in any other New Testament passage. We don’t find one occasion when Peter claimed authority over the other apostles. Nor do we encounter one passage where the others acknowledged Peter as their superior. Further, when Paul went to Jerusalem to consult with the elders of the church about the “Jewish problem,” he met with three men who were equally viewed as pillars — James,Peter, and John (Galatians 2:9). No one man in the first century took to himself the authority that the Roman Catholic Church claims for the Pope.