Question: "What is the rock in Matthew 16:18?"
Answer: The debate rages over whether "the rock" on which Christ will build His church is Peter, or Peter's confession that Jesus is "the Christ, the Son of the Living God" (Matthew 16:16). In all honesty, there is no way for us to be 100% sure which view is correct. The grammatical construction allows for either view. The first view is that Jesus was declaring that Peter would be the "rock" on which He would build His church. Jesus appears to be using a play on words. "You are Peter (petros) and on this rock (petra) I will build my church." Since Peter's name means rock, and Jesus is going to build His church on a rock " it appears that Christ is linking the two together. God used Peter greatly in the foundation of the church. It was Peter who first proclaimed the Gospel on the day of Pentecost (Acts 2:14-47). Peter was also the first to take the Gospel to the Gentiles (Acts 10:1-48). In a sense, Peter was the rock "foundation" of the church.
The other popular interpretation of the rock is that Jesus was referring not to Peter, but to Peter's confession of faith in verse 16: "You are the Christ, the son of the living God." Jesus had never explicitly taught Peter and the other disciples the fullness of His identity, and He recognized that God had sovereignly opened Peter's eyes and revealed to him who Jesus really was. His confession of Christ as Messiah poured forth from him, a heartfelt declaration of Peter's personal faith in Jesus. It is this personal faith in Christ which is the hallmark of the true Christian. Those who have placed their faith in Christ, as Peter did, are the church. Peter expresses this in 1 Peter 2:4 when he addressed the believers who had been dispersed around the ancient world: "Coming to Him as to a living stone, rejected indeed by men, but chosen by God and precious, you also, as living stones, are being built up a spiritual house, a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ."
At this point, Jesus declares that God had revealed this truth to Peter. The word for "Peter," Petros, means a small stone (John 1:42). Jesus used a play on words here with petra ("on this rock") which means a foundation boulder, as in Matthew 7:24, 25 when He described the rock upon which the wise man builds his house. Peter himself uses the same imagery in his first epistle: the church is built of numerous small petros "living stones" (1 Peter 2:5) who, like Peter, confess that Jesus is the Christ, the Son of the living God, and those confessions of faith are the bedrock of the church.
In addition, the New Testament makes it abundantly clear that Christ is both the foundation (Acts 4:11, 12; 1 Corinthians 3:11) and the head (Ephesians 5:23) of the church. It is a mistake to think that here He is giving either of those roles to Peter. There is a sense in which the apostles played a foundational role in the building of the church (Ephesians 2:20), but the role of primacy is reserved for Christ alone, not assigned to Peter. So, Jesus' words here are best interpreted as a simple play on words in that a boulder-like truth came from the mouth of one who was called a small stone. And Christ Himself is called the "chief cornerstone" (1 Peter 2:6, 7). The chief cornerstone of any building was that upon which the building was anchored. If Christ declared Himself to be the cornerstone, how could Peter be the rock upon which the church was built? It is more likely that the believers, of which Peter is one, are the stones which make up the church, anchored upon the Cornerstone, "and he who believes on Him will by no means be put to shame" (1 Peter 2:6).
The Roman Catholic Church uses the argument that Peter is the rock to which Jesus referred as evidence that it is the one true church. As we have seen, Peter's being the rock is not the only valid interpretation of this verse. Even if Peter is the rock in Matthew 16:18, this is meaningless in giving the Roman Catholic Church any authority. Scripture nowhere records Peter being in Rome. Scripture nowhere describes Peter as being supreme over the other apostles. The New Testament does not describe Peter as being the "all authoritative leader" of the early Christian church. Peter was not the first pope, and Peter did not start the Roman Catholic Church. The origin of the Catholic Church is not in the teachings of Peter or any other apostle. If Peter truly was the founder of the Roman Catholic Church, it would be in full agreement with what Peter taught (Acts chapter 2, 1 Peter, 2 Peter).