The argument that Jesus was the only Rock and not Peter is false. When Jesus called Simon, He called him (Cephas/Kephas) which are transliterations of the Aramaic word Kepa, which means ROCK. So yes, Jesus is the ROCK and this same Jesus, in Aramaic, called Simon, ROCK. Jesus is the one who called Simon, Rock and so those who have a problem with Peter being called Rock, need to take it up with Jesus.
“He first found his own brother Simon and told him, ‘We have found the Messiah’ (which is translated Anointed). Then he brought him to Jesus. Jesus looked at him and said, ‘You are Simon the son of John; you will be called Kephas [Rock]’” (Jn 1:42).
Teresa Stark Riordan says: Scripture uses three different "rock" metaphors. God is the "rock" of our salvation (Deut 32:15; Ps 62:2). Abraham is the "rock" from which the Jewish people were hewn (Isaiah 51:1).
Peter is the "rock" on which the Church is built (Matt 16:18). To argue that "Peter can't be the rock because God is the rock" makes no more sense than to argue "God can't be the rock because Abraham is the rock." They are different metaphors.
Peter's being the "rock" on which the Church is built does not detract from God being the "rock" of our salvation.
Fernando Uano Commentary: Here are verses that mentions the Aramaic word CEPHAS (Simon Peter).
1Cor.1  What I mean is that each one of you says, "I belong to Paul," or "I belong to Apol'los," or "I belong to Cephas," or "I belong to Christ."
1Cor.3  whether Paul or Apol'los or Cephas or the world or life or death or the present or the future, all are yours;
1Cor.9  Do we not have the right to be accompanied by a wife, as the other apostles and the brothers of the Lord and Cephas?
1Cor.15  and that he appeared to Cephas, then to the twelve.
Gal.1  Then after three years I went up to Jerusalem to visit Cephas, and remained with him fifteen days.
Linwood Kemp quotes the Apostle Paul and says, "For no other foundation can anyone lay than that which is laid, which is Jesus Christ" (1 Cor. 3:11).
Is there anything ambiguous about that? When he asked this question, he is really asking a rhetorical question, which is really not a question but a statement. He is in effect saying, no, there is really nothing ambiguous about that. And in this, to his compliment, he is totally straight forward and correct.
Jesus is the foundation; however, is it Jesus alone who comprises the foundation? According to Paul, the foundation is also comprised of the Apostles and prophets. "You are built upon the foundations of the APOSTLES and PROPHETS, and Christ Jesus himself is the cornerstone" (Ephes 2:20).
Yes, Linwoods point is well made; Jesus is the foundation and the Apostles and prophets are a part of it, and Jesus is the cornerstone. And so it is NOT JESUS ALONE; it is also a foundation comprised of APOSTLES and PROPHETS. Thank you for your commentary Linwood; it is most appreciated.
Aldo Lombardi does not believe that Peter can be the rock because Paul says, "the rock was Christ" (1 Cor 10:4). He is reasoning that if Jesus is the Rock then Peter cannot be the rock of Christ’s Church. And of course Aldo is correct; Jesus is the Rock. However, Aldo leaves out the fact that this same Rock (Jesus), called Simon Peter rock (Kephas) in Aramaic. "Then he brought him to Jesus. Jesus looked at him and said, ‘You are Simon the son of John; you will be called Kephas [Rock]” (Jn 1:42). I can believe Aldo, who claims that Peter is not the rock (Kephas), or I can believe Jesus, who called Simon Peter, Rock. Who will you believe?
Unless the Lord builds the house, they labor in vain. Leena Gouin questions, "How many foundations can a house have? " And then answers her own question, "We can only have one foundation." Leena is correct, there is only one foundation; however, she fails to acknowledge, there can be many stones (apostles & prophets) in this SAME foundation, with Christ Jesus as the cornerstone! "You are built upon the foundations of the APOSTLES and PROPHETS, and Christ Jesus himself is the cornerstone" (Eph 2:20). How do they get around Ephesians 2:20; they simply ignore it and only quote, (1 Cor 3:11).
You cannot get around the fact that Jesus called Peter Rock (kephas or Cephas) when he first called Peter. It is very difficult for some to believe, but this was no difficulty for Jesus since He is the one who called Peter Rock.