The pope only speaks exceedingly rarely excathedra, infallibly, but some believe it’s a daily occurrence. It’s not.
We believe that Christ, himself, did the first ordinations, if you will, when he breathed on them, giving them authority to forgive sin. After the resurrection, Christ said all power and authority on heaven and earth had been given to him. Jesus turned to Peter and asked him, and him alone, 3 times, to shepherd the sheep. Jesus said Simon would be Peter, the rock on which he would build his Church, that the gates of hell would not prevail against it.
Peter was the apostle’s clear leader in the absence of Jesus. Peter spoke for them, on their behalf. He was always listed as the first, and foremost, apostle. Jesus told Peter that it’d be necessary later that he go back and strengthen his brethren.
When there were any concerns or disputes, when Peter spoke, it was considered final.
Peter’s was the first of the miracles of the apostles.
Christ gave Peter alone the “keys of the kingdom”. Keys are a symbol of authority. Jesus told Peter that what he held bound on earth would be bound in heaven.
Now, when Judas committed suicide, he was replaced by Matthew. These were positions that we’d refer to in our, modern, times as “offices”. When Peter left, authority was passed to someone else.
Do we need a pope? Yes. We need some kind of leadership. When Christ was on earth, he was the leader. When Christ ascended, Peter was the Church’s leader, but Christ never intended his Church to be leaderless.
Some other churches have done away with the pope, only to have their own leaders, their own “popes”, although they don’t use that word, calling them other names, instead. At least, our pope is leading by divine authority.
Now, we believe Jesus is still guiding his Church, even now. Some other churches don’t have any leader, and when they have questions on matters of faith, in these leaderless churches, there is no one with authority to answer these questions, make decisions, or even call a council.
It’s a matter of faith to us, the pope, infallibility. In 2,000 years, we have used this system that Christ, himself, set up. The Catholic Church is actually the world’s longest lasting institution, and we don’t think that’s by accident. People study the Church to find out what its secret of longevity is, but we believe it’s due to God’s guidance.
We take, on faith, Christ’s word. We accept the representatives he has given us. I believe if we reject his representatives, we reject Christ. If we reject Christ, we reject the one who sent him.