“And upon this rock … - This passage has given rise to many different interpretations. Some have supposed that the word ‘rock’ refers to Peter’s confession, and that Jesus meant to say, upon this rock, this truth that thou hast confessed, that I am the Messiah and upon confessions of this from all believers, I will build my church. Confessions like this shall be the test of piety, and in such confessions shall my church stand amid the flames of persecution, the fury of the gates of hell. Others have thought that Jesus referred to himself. Christ is called a rock, Isaiah 28:16; 1 Peter 2:8. And it has been thought that he turned from Peter himself, and said, ‘Upon this rock, this truth that I am the Messiah and- upon myself as the Messiah, I will build my church.’ Both these interpretations, though plausible, seem forced upon the passage to avoid the main difficulty in it. Another interpretation is, that the word ‘rock’ refers to Peter himself.
This is the obvious meaning of the passage; and had it not been that the Church of Rome has abused it, and applied it to what was never intended, no other interpretation would have been sought for. ‘Thou art a rock. Thou hast shown thyself firm, and suitable fir the work of laying the foundation of the church. Upon thee will I build it. Thou shalt be highly honored; thou shalt be first in making known the gospel to both Jews and Gentiles.’ This was accomplished. See Acts 2:14-36, where he first preached to the Jews, and Acts 10, where he preached the gospel to Cornelius and his neighbors, who were Gentiles. Peter had thus the honor of laying the foundation of the church aming the Jews and Gentiles; and this is the plain meaning of this passage. See also Galatians 2:8. But Christ did not mean, as the Roman Catholics say he did, to exalt Peter to supreme suthority above all other apostles, or to say that he was the only one upon whom he would rear his church. Ser Acts 15, where the advice of James, and not that of Peter, was followed. See also Galatians 2:11, whete Paul withstood Peter to his face, because he was to be blamed - a thing which could not have happened if Christ (as the Roman Catholics say) meant that Peter was absolute and infallible. Mire than all, it is not said here, or anywhere else in the Bible, that Peter would be the viceregents of Christ and the head of the church. The whole meaning of the passage is this: ‘I will maje you the honored instrument of making known my gospel first to Jews and Gentiles, and I will make you a firm and distinguished preacher in building my church.’”
(
Barnes’ Notes on the Bible)