Can you provide citations for those quotes? I don't doubt that they're genuine, but since we're reading translations into English it might be helpful to know the exact reference so that comparisons to different translations can be made for the sake of clarity. None of the quotations prove that papal infallibility was taught or believed in the early centuries. At best, what those writers said is consistent with Vatican I, but most of it is also consistent with the Eastern Orthodox and Protestant positions as well. Everyone recognizes that Rome was a bastion of Orthodoxy when the rest of the world was engulfed successively in the Arian, Nestorian, and Monophysite controversies. Beyond that, the case is overstated: Hormisdas and Maximus, in the translations you quoted, said that Rome had not erred, not that Rome could not err. What initially brought Pope Gregory into conflict with Patriarch John was the Pope's (quasi-)appellate jurisdiction, which would be meaningless if he also had ordinary universal jurisdiction.