Thou art Peter, and upon this rock, I will build my Church, and the gates of Hell shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven. (Matthew 16:18-19)Saint Peter was, perhaps the most obviously bumbling of the apostles. There has even been talk, in modern times, of St. Peter possibly suffering from something like ADHD, so impulsive were his actions.
And yet, Jesus chose Peter to lead the apostles after His death, and to serve the newborn Church in its first years. Why? Peter was an uneducated fisherman. He was impulsive. He denied Christ three times.
Perhaps Christ chose Peter to lead the Church precisely because of his apparent inability. Before Christ handed over the keys to the Kingdom of Heaven to Peter, Peter went through, what must have been a kind of "dark night of the soul". After vehemently promising to die for Christ, Peter denied Him three times, then went out and wept bitterly. He then joined the other Apostles (except for St. John) in running away while their Savior was crucified.
Who in the world would have chosen Peter to lead the Church?! Jesus. He knew Peter was the apostle through whom He could shower His graces and lead people to Himself just as God chose Moses, who described himself as "slow of speech" (Exodus 4:10) to lead His people out of Egypt.
By choosing these imperfect men, God shows His power, grace and mercy. Those who say that Peter, and his successors the popes, are fallible human beings are exactly right. In spite of their obvious humanity, God has chosen them to carry on His work in the Church, even today. In spite of all their obvious failings over the centuries, the Church still stands, as a testament to God's promise,
The gates of Hell shall not prevail against it.