Hey RedFan,
In your first sentence you say that you know the history of the church but by the end of your post you ask a question that indicates you don't know the history of the church.
The short answer to your question is Peter was the bishop of Rome and he was the head of The Church after Jesus death. Peter's successor would then be head of The Church and bishop of Rome!
The long answer is here
Primacy of Rome
Thanks for sharing. Yes, I was already aware of all of these writings. I have traced how the Papacy gained ascendancy in the West, and not in the East.
Through Irenaeus’s
Against Heresies (Book III, Chapter 3) we can trace the succession of Roman bishops, but not any serious argument for Roman primacy over the Church at large, i.e., beyond the See of Rome. He calls it “a matter of necessity that every Church should agree with this (Roman) Church, on account of its preeminent authority,” but offers no reason why this should be so. Absent any early mention of such a transfer of worldwide leadership authority to Rome, we might look for some written record showing that in the first several centuries of Christianity believers throughout the rest of the Mediterranean world recognized the Bishop of Rome as having primacy over other bishops. I actually find the opposite to be true:
First, the writing most pointed to on the subject is the Epistle of Clement of Rome to the Church at Corinth, toward the end of the First Century, urging the Corinthians not to depose their own leaders. I find this equivocal at best. Some have argued that because it responds to a matter on which the Corinthians had apparently consulted Rome, these Corinthians must have recognized Rome’s authority. But read its tenor, and one thing jumps out:
this is not the writing of a man who thought he could impose his will in Greece. (Indeed, in chapter 56 he suggests to the dissenting Corinthians that “they should submit themselves,
I do not say unto us, but unto the will of God.”)
Second, in the middle of the third century, Pope Stephen’s view regarding the efficacy of baptism by heretics was rejected by 87 bishops at a Council of Carthage, at which Cyprian stated: “For neither does any of us set himself up as a bishop of bishops, nor by tyrannical terror does any compel his colleague to the necessity of obedience, since every bishop, according to the allowance of his liberty and power, has his own proper right of judgment, and can no more be judged by another than he himself can judge another.”
Third, there is evidence of various sees (Rome, Antioch, Alexandria) having authority over neighboring provinces or otherwise associated bishoprics, but with complete autonomy in their own spheres, i.e., Alexandria and Antioch gave no deference to Rome. In 325 the Council of Nicaea produced, aside from its famous Creed, about twenty canons, the sixth of which suggests if not confirms the equal standing of these three sees.
It is reasonable to conclude that in mid-Fourth century Rome had no jurisdiction over eastern bishoprics. Afterwards the notion gained traction, but never complete acceptance . The schism that eventually split Eastern Orthodoxy and the Western Church proves that it never gained complete support. But my point is that the primacy of the Bishops of Rome (beyond Peter)
cannot be traced back to the traditions of the early Church. And I a a big fan of Irenaeus!