Petros (Peter) a stone or boulder, and petra (a large mass of rock) are not the same thing.
Apparently Peter missed the point as well when he wrote in 1 Peter 2: 4-8 that Jesus was the stone on which the church was built. Peter never claimed it for himself. If the Catholic church wrote the Bible, how could it make such a serious oversight?
1 Peter 2
4As you come to him, a living stone rejected by men but in the sight of God chosen and precious, 5 you yourselves like living stones are being built up as a spiritual house, to be a holy priesthood, to offer spiritual sacrifices acceptable to God through Jesus Christ. 6For it stands in Scripture:
“Behold, I am laying in Zion a stone,
a cornerstone chosen and precious,
and whoever believes in him will not be put to shame.”
7So the honor is for you who believe, but for those who do not believe,
“The stone that the builders rejected
has become the cornerstone,”
8and
“A stone of stumbling,
and a rock of offense.”
There is no usage of "petros" as small rock in patristic Greek. It is a rare word. "Petra" is rock, and Petros is simply a masculine form of "petra". It is clear form the passage that Jesus praised Peter's faith and so renamed him after the Rock on which He will build His church.
Indeed, that does not make Jesus Himself any less of a "rock of our salvation". What is shows is that St. Peter was chosen as some kind of a human fundament for the Church. That is what the Papacy is.
1 Peter 2:5, by the way, uses another word, "lithoi".