How does the Catholic Church explain their belief that Jesus chose Peter to build upon? Jesus was God and knew well the character and faults of Peter his disciple. The gospels give us a look at his impetuosity, asking Jesus 'if it is you, tell me to walk on the water';  arrogance, wanting to call fire down from heaven; cowardice, denying the Lord; etc.

Since there are alternate explanations and meanings for Matthew 16:18 (most non-Catholic Christians think the 'rock' Jesus built His church on is Jesus Himself, or the revelation of who Jesus is, that the Father gave to Peter) why does the Catholic Church adhere to their point of view, calling Peter the foundation that Jesus built his church on? Why would Jesus himself not be the Rock?
Jesus was God and knew well the character and faults of Peter his disciple. The gospels give us a look at his impetuosity-asking Jesus 'if it is you, tell me to walk on the water', arrogance - wanting to call fire down from heaven, cowardice- denying the Lord, etc.

None of the twelve apostles were perfect. One doubted, one betrayed, one denied and all of them deserted him in the time when he most needed them. These men are far from perfect. Yet, in spite of themselves, God used them powerfully to change the known world in a single generation.

Since there are alternate explanations and meanings for Mathew 16:18

I don't know what alternative point of view you are talking about. But As far as I know, Jesus changed his name to Cephas (Yes, Cephas - as in Galatians 2:7-14, I Cor. 1:11-13, I Cor. 3:21, I Cor. 9:5 and I Cor. 15:5 meaning Rock not a pebble) has no other reasonable explanation. (Unlike James and John - the sons of thunder - , Cephas is not a name that denotes Peter's Character).

Peter seems unlikely as a foundation for the whole church .... Peter is not only unlikely from his character flaws that we see revealed in the gospels.

But the Lord said to Samuel, “Do not look on his appearance or on the height of his stature, because I have rejected him. For the Lord sees not as man sees: man looks on the outward appearance, but the Lord looks on the heart.” (1 Samuel 16:7)

But there could be many reasons why Jesus Chose Peter.


Peter had a natural leadership skills (John 21:3)
He was the first to act (John 20:6, John 21:7)
He loved the Lord so much. (John 21:17)


...but any human person seems unlikely as a suitable foundation for the whole church of Jesus on the earth... why does the Catholic Church adhere to this point of view? What is the reason that the CC adheres to this idea that Peter could be the foundation for the whole church of Jesus?

Probably because Jesus himself said that he will built his Church on him and even went on to change his name as a proof of it. In the Bible, name of a person is changed by God when they are called to lead a significant role. (Like Abram-Abraham/Jacob-Israel) If Peter was just one of the twelve, this event is an anomaly.

Also all thru the New Testament, Peter's Primacy is shown in hidden symbols. Like for example,

In Gospels


Peter's name appears first in every list of the twelve. Mathew even says he was the first (Mat 10:2)
When evangelists mention the apostles, Peter is unusually singled out (Mark 1:36, Mark 16:7, Luke 9:32)
Peter is approached by the temple authorities as a representative of the Group. (Mt 17:24-27 - Note this is the only place in the NT where Jesus refers himself in equal level with another human being. Jesus says '(Pay the tax for) me and for yourself')
Peter often spoke to Jesus on behalf of the twelve. (Mk 8:29; Lk 12:41; Jn 6:66-69)
At the Last supper, Even though Satan has asked to sift all of them, Jesus says he prayed for Peter specifically and asks him to strengthen others after regaining his own faith (Lk 22:31-32)
John waited for peter to enter into the tomb. (John 20:6)
Among the Apostles the resurrected Lord appeared first to Peter. (Luke 24:34; 1 Cor 15:5)
Jesus made promises to Peter that he had not made to other Apostles. (Mt 16: 18-19; Rock/Keeper of Keys of Kingdom)
Peter alone was given in charge to be the head shepherd (Jn 21:15-17)


In Acts


Peter initiated and oversaw the replacement of Judas (Acts 1:15-26; Note that this happened before the decent of the Holy Spirit, i.e., he is acting on his own authority, given to him by Jesus)
Peter delivered the inaugural sermon of Church History (Acts 2:14-36; First to preached and administered Baptism to the chosen people after resurrection)
Peter was the first to preach and administered Baptism to the Gentiles (Acts 10:1-48)
Peter performed the first healing after the resurrection. (Acts 3:1-10)
Peter was the first to discipline (Acts 5: 1-11)
Peter was the final authority in the first council of Jerusalem (Acts 15: 6-11)


In New testament


Of all the twelve apostles Peter is mentioned more times than all other apostles put together. (Peter - 195 times; Other Apostles 130 times)


No other apostles has this unique mission of leading the Apostles/early Church as evident in the Bible.

[P.S: Also in your previous version of your question, you seem to confuse cornerstone with foundation rock. Corner stone is placed on Foundation rock to built upon. Both are different.]