Matthew 16:15 “Who do you say I am?”
16 Simon Peter answered, “You are the Christ, the Son of the living God.” **
17 Jesus replied, “Blessed are you, Simon son of Jonah, for this was not revealed to you by man, but by my Father in heaven. 18 And I tell you that you are Peter, and on this rock ( the Christ, the Son of the living God. **) I will build my church,
There is more to the passage than what you posted.
Matthew 16:[15] He said to them, “But who do you say that I am?”
[16] Simon Peter replied, “You are the Christ, the Son of the living God.”
[17] And Jesus answered him, “Blessed are you, Simon Bar-Jona! For flesh and blood has not revealed this to you, but my Father who is in heaven.
[18] And I tell you, you are Peter, and on this rock I will build my church, and the powers of death shall not prevail against it.
[19] I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven.”
Jesus goes on to day that He is giving Peter the keys of the kingdom and the authority to bind and loose.
This passage takes place near Caesarea Philippi where there was a rock cliff which was a pagan temple to Pan.
http://www.welcometohosanna.com/LIFE_OF_JESUS/lifejesuspix/CaesareaPhilippiSacredComplex.jpg
Jesus could have been using this as a backdrop to give meaning to what he is telling Peter.
Jesus was saying that ‘Simon you are rock and on this rock I will build my church.’
He is giving Peter authority over his church here on earth once Jesus is in heaven.
Giving Peter the keys is making him the Prime minister once the King is away, just as Isaiah 22 speaks of the keys to the kingdom.
You are correct that Jesus is the rock, and the cornerstone, but Jesus in not trying to make that point in this passage.
Keep in mind that Jesus says that He is building His Church, not Peter’s Church.