Catholics can accept the view that Christ founded the Church on the faith of Peter. However, we reject the notion that that is all Christ intended.
Pope
Peter and the Papacy: Feed My Sheep
Peter and the Papacy: In today’s gospel, Jesus takes Peter back to that moment in time when, at a charcoal fire, he denied him three times. But now, before this new charcoal fire, things are very different.
Even In The Midst of Turmoil and Confusion, I Thank God for St. Peter and The Papacy
I’m well aware of the turmoil, conflict and division that has reared its ugly head during the reign of Pope Francis. Even so, I thank the Lord Jesus Christ for the papacy and the hierarchical structure of the Spirit-guided Church.
Pope Benedict: To Make Christ Known Is A Most Precious Gift
Because of what we have received through the gift of faith, we are compelled to offer our life, our very self, as a gift to Christ and thus become instruments of his glory, which is accomplished by our complete cooperation in docility with the impulses of the Spirit, whom the Savior gives to those who love him.