On him [Peter] he [the Lord] builds the Church, and commands him to feed the sheep, and although he assigns a like power to all the apostles, yet he founded a single chair, 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 [cathedra]… 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.
This, citation and all, is taken from Jimmy Akins book
The Fathers Know Best. I wanted to throw this quote out there just so that it is clear that they aren’t all taken out of context, and will leave the rest of the debate to people more familiar with the writings concerned. (I am also aware that this text by itself does not prove anything because individual Fathers aren’t infallible, and even if they were that it doesn’t explicitly say that the Pope has any particular powers, but it does hint rather strongly that there is more than a primacy of honor going on.)