A common belief of millions of professing Christians is that Peter was designated by Jesus to be the foundation or head of the church. Because of this, great honor is paid to Peter to this day by these same professed believers. When asked why they believe this, many will quote Matthew 16:18-19 as the answer, explaining that Jesus said Peter was the rock on which the church would be built. If this is true, why did Jesus say Peter was the rock on which the church would be built? To answer this, the text in context of Matthew 16 needs to be studied.
What is the context of Matthew 16?
Jesus had just arrived with the disciples at Caesarea Philippi, about 25 miles north of the Sea of Galilee. He had just left Magdala, which was on the western shore of the Sea of Galilee, where he had just debated with the Pharisees and Sadducees  who wanted him to produce a sign from heaven to verify who He was. Jesus warned the disciples to beware of the leaven of the Pharisees and of the Sadducees. The disciples did not understand what he meant by warning them to beware of leaven. Jesus explained to them how He had earlier told them not to beware of the leaven of the bread miraculously produced, but of the doctrine of the Pharisees and of the Sadducees. This encounter left the disciples with the idea of people wondering who Jesus was in their minds.
What did Jesus mean by building His church upon a rock?
At Caesarea Philippi, Jesus expounded upon this thought when He asked the disciples, “Whom do men say that I the Son of man am?” Their answers varied. They said that some said that He was John the Baptist, Elijah, Jeremiah, or one of the prophets. Jesus then asked them directly, “But whom say ye that I am?” Simon Peter answered and said, “Thou art the Christ, the Son of the living God.” Jesus responded to Peter by saying, ‘Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven. And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven’” (Matthew 16:17-19).
So, what did Jesus mean when He referred to building His church upon this rock? First, Jesus stated that Peter did not come up with his answer on his own, but that it was revealed to him by God the Father in heaven. Second, when Jesus said, “…thou art Peter, and upon this rock I will build my church…”, He was making two linguistic points. The first point was a comparison of the name Peter to the word rock. The New Testament was written in Greek. The name Peter in Greek is petros, meaning a pebble or small stone. The word for rock in the Greek is petra, meaning a massive rock or bedrock. Jesus was making the linguistic point that this simple truth that God had revealed to Peter, the pebble, about Jesus being the Christ, the rock.
The second linguistic point was that the rock was the foundation or bedrock upon which He would build His church. This was a reference to salvation through Jesus the Christ. This is referred to in several other passages as follows:
Therefore thus saith the Lord GOD, Behold, I lay in Zion for a foundation a stone, a tried stone, a precious corner stone, a sure foundation: he that believeth shall not make haste. (Isaiah 28:16)
Whosoever cometh to me, and heareth my sayings, and doeth them, I will shew you to whom he is like: He is like a man which built an house, and digged deep, and laid the foundation on a rock: and when the flood arose, the stream beat vehemently upon that house, and could not shake it: for it was founded upon a rock. But he that heareth, and doeth not, is like a man that without a foundation built an house upon the earth; against which the stream did beat vehemently, and immediately it fell; and the ruin of that house was great. (Luke 6:47-49)
For we are labourers together with God: ye are God’s husbandry, ye are God’s building. According to the grace of God which is given unto me, as a wise masterbuilder, I have laid the foundation, and another buildeth thereon. But let every man take heed how he buildeth thereupon. For other foundation can no man lay than that is laid, which is Jesus Christ. (1 Corinthians 3:9-11)
Now therefore ye are no more strangers and foreigners, but fellowcitizens with the saints, and of the household of God; And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone; In whom all the building fitly framed together groweth unto an holy temple in the Lord: In whom ye also are builded together for an habitation of God through the Spirit. (Ephesians 2:19-22)
Therefore leaving the principles of the doctrine of Christ, let us go on unto perfection; not laying again the foundation of repentance from dead works, and of faith toward God, (Hebrews 6:1)
See also Ephesians 1:15-23; Ephesians  4:15-16; Ephesians 5:23; 1 Peter 2:1-8
It is clear from these passages that the church was built upon Jesus Christ, not Peter. Consider for a moment what Jesus said just afterwards to Peter in Matthew 16:20-23. Jesus told the disciples not to tell anyone that He was the Christ. Then Jesus started explaining how He must go in to Jerusalem to suffer and be killed and be raised again on the third day. When Peter heard this, he rebuked Jesus! Peter told Jesus to stay away from there so that it doesn’t happen to Him. Jesus responded by telling Peter “Get thee behind me, Satan: thou art an offence unto me: for thou savour rest not the things that be of God, but those that be of men” (Matthew 16:23).
Focusing on what Jesus said to Peter, it is hard to believe that Jesus would have meant that He was going to build His church on Peter, whom He referred to as Satan and an offense. To suggest otherwise, would mean that Jesus was mistaken about Peter or that Jesus would build His church on satanic man-made values with Peter as the head. While it is clear that some churches have built their foundation on satanic man-made values, this was not the foundation that Jesus built the church upon.
Many professing Christians believe that Peter was designated by Jesus to be the foundation or head of the church. They base their belief on an out of context interpretation of Matthew 16:17-19. Instead, Jesus referred to Peter being a small pebble that understood the real foundation of the church, Jesus Christ. Reading this passage in proper context along with supporting verses shows us that Jesus is the Christ, the Rock of our salvation.
Read more about Peter here: Apostle Peter Biography 
Resources – Scripture quotations are from The Holy Bible, King James Version