I get in these long discussions way too much. I'll just drop a passage from the early Christians and you figure it out.

The Lord says to Peter: “I say to you,” he says, “that you are Peter, and upon this rock I will build my Church, and the gates of hell will not overcome it. And to you I will give the keys of the kingdom of heaven . . .” [Mt 16:18–19]. On him he builds the Church, and commands him to feed the sheep [Jn 21:17], and although he assigns a like power to all the apostles, yet he founded a single chair [cathedra], and he established by his own authority a source and an intrinsic reason for that unity. Indeed, the others were also what Peter was [apostles], but a primacy is given to Peter, by which it is made clear that there is one Church and one chair. . . . If someone does not hold fast to this unity of Peter, can he think that he holds the faith? If he deserts the chair of Peter upon whom the Church was built, can he be confident that he is in the Church? - St. Cyprian of Carthage [Unity of the Catholic Church 4; first edition (Treatise 1:4) (A.D. 251)].