Excellent answers to this question at:
Catholicism and the Primacy of the Pope"According to Jesus, Peter?s confession that Jesus is ?the Christ, the Son of the living God? is ?the rock,? upon which Jesus will build His church. Conversely, Rome asserts that the ?rock? upon which Jesus will build His church is the Apostle Peter, not his confession. This erroneous interpretation can be shown as (a) exegetically false and (b) historically problematic."
Matthew
16:15 He saith unto them, But whom say ye that I am?
16:16 And Simon Peter answered and said, Thou art the Christ, the Son of the living God.
16:17 And 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.
16:18 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. "Christ, you see, built his Church not on a man but on Peter?s confession. What is Peter?s confession? ?You are the Christ, the Son of the living God.? There?s the rock for you, there?s the foundation, there?s where the Church has been built, which the gates of the underworld cannot conquer (Sermons, XI, Sermon 229, 327). historian, Eusebius of Caesarea (A.D. 263-339),
I
saiah 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.
Ephesians 2:19-20 the household of God; are built upon the foundation of the apostles and prophets, Jesus Christ himself being the chief corner stone;