This is where I feel misunderstood and this has been my point all along - The claim is that Peter is the first Pope, the first leader of the New Testament church, the claim is that modern Catholics are following an uninterrupted chain from the original "One, Holy, Catholic, Apostolic church." But how do you account for the vast differences in the teachings of Peter and the Apostles (Apostolic) from Catholic Dogma?
For example Mary... she was around and would have been fulfilling many of the roles that many on this thread claim she carried - yet there is no evidence in scripture that Peter, nor the Apostles, venerated her in the way, or even remotely near the way, men do today.
In Acts 2:38, and all throughout the New Testament Peter baptizes in "the name of Jesus Christ" yet Catholics accept trinity.
Catholic accepted practice forbids marriage for the clergy, yet Peter, Paul, and other new testament leaders were married.
I don't mean to make a list of apparent Catholic vs. Bible contradiction (there are many more), but I do aim to support my assertion that calling Peter the first pope and claiming to be descendants of the Apostolic church should mean that you are following the lead set by Peter and the Apostles
The simple answer is that God has been active in the world since 96 AD, the Holy Spirit dwells in the Church and continues to direct it, and there has been a great deal more revealed and developed and simple happenings since then. The Bible is an incomplete record. That which happened afterwards is not in it. The Catholic Church has indeed been continuously in operation since those days, with the Apostolic succession and the Holy Spirit, and it has the authority to update our understanding precisely BECAUSE it speaks with the authority of God.
Jesus updated Judaism, which became so hidebound with tradition that it could not accept new revelation. The Church Jesus left continues to update itself based on the ongoing revelations from God.
In the New Testament period, Mary was not being sent by God from heaven as his emissary, because it was not time to do that yet, the Apostles were in the world still, and the Church was moving in a pagan and extremely masculine society.
Her first great emissary work was to Aztec Guadelupe, a society and civlization that had a much stronger principle of feminine authority and that was, therefore, willing to listen to her. The Lord chooses his instruments according to his needs, and human beings and their societies are variable.
That's why it's not in the Bible.
For you, a Protestant, the Bible is the only source of authority. For Catholics, God is the authority, and revelation has continued through the Church. Prophesy, miracle, and revelation, and divine intervention, did not end in the First Century with the Apostles. They continue forward into the Twenty First, and the Church has to observe and react to each new thing under the Son that God does.