Here is the text in question:
13When Jesus came into the coasts of Caesarea Philippi, he asked his disciples, saying, Whom do men say that I the Son of man am?
14And they said, Some say that thou art John the Baptist: some, Elias; and others, Jeremias, or one of the prophets.
15He saith unto them, But whom say ye that I am?
16And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
17And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.
18And 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.
Now take a look at what scripture has that shows us clearly who it is:
Deuteronomy 32:3-4 Because I will publish the name of the LORD: ascribe ye greatness unto our God. He is the Rock, his work is perfect: for all his ways are judgment: a God of truth and without iniquity, just and right is he.
Deuteronomy 32:15,18 But Jeshurun waxed fat, and kicked: thou art waxen fat, thou art grown thick, thou art covered with fatness; then he forsook God which made him, and lightly esteemed the Rock of his salvation……Of the Rock that begat thee thou art unmindful, and hast forgotten God that formed thee.
What does this say…?
2 Samuel 22:32 For who is God, save the LORD? and who is a rock, save our God?
What does David say?…
Psalms 18:2 The LORD is my rock, and my fortress, and my deliverer; my God, my strength, in whom I will trust; my buckler, and the horn of my salvation, and my high tower.
Psalms 18:31 For who is God save the LORD? or who is a rock save our God?
Psalms 95:1 O come, let us sing unto the LORD: let us make a joyful noise to the rock of our salvation.
Isaiah 28:16 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.
And we read in Matthew:
Matthew 21:42 Jesus saith unto them, Did ye never read in the scriptures, The stone which the builders rejected, the same is become the head of the corner: this is the Lord’s doing, and it is marvellous in our eyes?
Luke 20:17 And he beheld them, and said, What is this then that is written, The stone which the builders rejected, the same is become the head of the corner?
And we read what Paul wrote:
Ephesians 2:20 And are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;
1 Corinthians 3:9-11 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 10:4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.
And from Peter himself:
1 Peter 2:4-6 To whom coming, as unto a living stone, disallowed indeed of men, but chosen of God, and precious, Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ. Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded.
Acts 4:8-12 Then Peter, filled with the Holy Ghost, said unto them, Ye rulers of the people, and elders of Israel, If we this day be examined of the good deed done to the impotent man, by what means he is made whole; Be it known unto you all, and to all the people of Israel, that by the name of Jesus Christ of Nazareth, whom ye crucified, whom God raised from the dead, even by him doth this man stand here before you whole. This is the stone which was set at nought of you builders, which is become the head of the corner. Neither is there salvation in any other: for there is none other name under heaven given among men, whereby we must be saved.
The Bible is clear and in complete harmony that Christ is the only rock and we are but stones which are built upon him. Now perhaps the best evidence that Christ did not appoint Peter as the “rock” on which He would build His church is the fact that none of those who heard Christ upon this occasion— not even Peter— construed His words in that way, either during the time that Christ was on earth or later. Had Christ made Peter chief among the disciples, they would not have been involved in repeated arguments afterward about which of them “should be accounted the greatest”.