Peter is the rock, and holds the keys
So then you are no longer strangers and foreigners, but you are fellow citizens with the saints, and of the household of God, being built on the foundation of the apostles and prophets, Christ Jesus himself being the chief cornerstone; in whom the whole building, fitted together, grows into a holy temple in the Lord; in whom you also are built together for a habitation of God in the Spirit.
Ephesians 2:19-22In context. Paul to the Ephesians on what Gentile believers now are: fellow citizens, a household built on the foundation of the apostles and prophets, with Christ Jesus himself the chief cornerstone.
Scripture states it. Jesus renames Simon, says “on this rock I will build my assembly”, and gives him the keys. In the usual sense of the wordplay the rock is Peter, as many Protestant scholars also hold; the confession and Christ readings need the referent to shift in mid-sentence. Binding and loosing is given to the disciples together (Matthew 18:18), and Paul names the apostles and prophets as the foundation, with Christ the cornerstone. Scripture is silent on the keys passing to a successor.
The Catholic reading
Jesus renames Simon and says he will build on “this rock”; a new name in Scripture marks a new role (Abram, Jacob). Then he gives him the keys, which in Isaiah 22:22 belong to the steward over the king’s house, an office refilled when its holder dies.
“The Lord made Simon alone, whom he named Peter, the "rock" of his Church.”
Catechism of the Catholic Church 881
The Protestant reading
The fathers read the rock three ways: Peter, Christ, and the confession. If the rock is Peter, he is a foundation stone laid once, like the other apostles in Ephesians 2:20. Revelation 3:7 gives the key of David to Christ himself, and after Pentecost and Cornelius the keys are never mentioned again.
“we err if we say that Peter himself is not in any sense a rock upon which the church is built”
Ligonier devotional, Peter, the Rock, 2008