A simple reading of history tells us that the Roman Catholic Church was not founded by Jesus - it was founded by Peter, in whom Jesus trusted the building of his church.
Peter was just a man, and therefore, was fallible. The church was and is staffed with mere mortal men, who are fallible. If Jesus was the one who chose the texts and letters that became the Old & New Testament, and if Jesus had been the person to lay down canon law, and if he were still running the outfit, then it would be infallible.
In no twisted interpretation of Scripture do I believe that Christ would have founded a church that promoted the likes of Pope Alexander VI to be the head of the church... or that would shelter so many pedophiles as we’ve seen recently.
“Infallible” does not mean “sinless.”
What is the name of the church you have found that has no sinners in it?
Isn’t the presumption that Jesus didn’t build his Church on Peter, a mere man as you state, but on continuing revelation from Jesus to his appointed leader? That the Rock is revelation, i.e. the direct word of God?