The root problem with making Peter the rock, is the ignorance of the revelation revealed in Matthew 16.
The question Jesus Asks Peter is this:

"But whom say ye that I am?"

The answer is revealed to Peter by God which is THE basis of the Gospel. Peter now believed something profound:

"Thou art the Christ, the Son of the living God."

You see, this revelation is supported by over a hundred scriptures on the answer for salvation, and it is guaranteed that we are saved by believing in WHO JESUS CHRIST IS & WHAT HE DID.

Peter did nothing for our salvation. It was all Christ.

If you want Peter as the rock, you have to re-write most of the Bible.

"TBA"
TBA

Greek dictionaries and lexicons give us further insight into the 2 words used in Matthew 16 for 'rock'

“…you are Peter (πέτρος, petros) and upon this rock (πέτρα, petra) I will build My church…”

Logically, you have obvious evidence that 2 different words are being used, regardless of their similar definitions. BUT... they are different.
So what's the difference?

1 - PETROS:

The definition of this form of rock, can be described as IMMOVABLE.
(Spiros Zodhiates, The Complete Word Study Dictionary: New Testament, electronic ed., G4074, Chattanooga, TN: AMG Publishers, 2000, c1992, c1993)

1 - PETRA:

The definition of this form of rock, can be described as EASILY MOVED.
Source: Vine, W., & Bruce, F. (1981; Published in electronic form by Logos Research Systems, 1996). Vine’s Expository Dictionary of Old and New Testament words (2:302). Old Tappan NJ: Revell

Peter was known to be 'unstable' having denied Jesus Christ 3 times, doubted when he walked on water and was rebuked by both Paul at Antioch & Jesus Himself.

And this is where the Catholic Catechism perverts things:

Our Lord then declared to him: “You are Peter, and on this rock I will build my Church, and the gates of Hades will not prevail against it.” Christ, the “living stone,” thus assures his Church, built upon Peter, of victory over the powers of death. Because of the faith he confessed Peter will remain the unshakeable rock of the Church. His mission will be to keep his faith from every lapse and to strengthen his brothers in it (552).

No! Peter, as much as he was merely the first to confess THE FAITH which identifies Jesus Christ (which is the foundation of our faith, THE immovable faith), was moveable just like any believer today.
The church are those believers who are in the true faith... the moveable rocks added to the foundation stone. We are built upon Christ, not Peter.