In those quotations Epiphanius and Irinaeus talk about Peter and Pul as founders of the Church, not as Bishops of the Church of Rome, is a big difference.
Eusebius of Caesarea
“[In the second] year of the two hundredth and fifth Olympiad [A.D. 42]: The apostle Peter, after he has established the church in Antioch, is sent to Rome, where he remains as a bishop of that city, preaching the gospel for twenty-five years” (The Chronicle [A.D. 303]).
I don’t think any of the other sources make such as claim as does Eusebius here who doesn’t take into account any other journeys where Peter founded the Church or his life in Jerusalem, he was married and had children, and the RCC actually makes no
claims for dating Peter’s episcopy in Rome,
the claim is that it’s because Peter died in Rome that his ‘sole episcopy’ passed down to his successors there.
I think we really need to understand that first otherwise none of the quotes used here will make sense. According to most traditions Peter died in Rome around 67 AD, if Eusebius is taken as simple fact then pre 42 AD Peter established the Church in Antioch and then went to Rome as its bishop.
What does Origen really say of Peter here, that he first went to Rome not long before he was martryred there? .
“Peter…at last, having come to Rome, he was crucified head-downwards; for he had requested that he might suffer this way.”
Origen,Third Commentary on Genesis,(A.D. 232) fragment in Eusebius 3:1:1,in NPNF2,X:132
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“[W]hat utterance also the Romans give, so very near(to the apostles), to whom Peter and Paul conjointly bequeathed the gospel even sealed with their own blood.”
Tertullian, Against Marcion,4:5(inter A.D. 207-212),in ANF,III:350
If you insist on placing Peter as bishop of rome pre his martrydom you’ll have a problem, as we’re saying the
early fathers had no concept of Rome’s claim to sole petrine primacy. If the importance of this particular succession was known to them do you think Tertullian would have written the above?
Peter and Paul **conjointly **bequeathed the gospel, not Peter and Paul taught there but Peter left his sole succession to the bishops in Rome and not to any other place he established the Church, rejecting Antioch his first see in favour of Rome…
If such a concept, as Rome has it, had existed in the early Church it would have been discussed, commented on, referred to specifically in every epistle having anything to do with Rome, but
there’s no such idea let alone teaching.
St Ignatius successor of Peter and Paul in Antioch wrote to the Church on his way to Rome and martyrdom, in his letter to Polycarp he reminds him that he has only God the Father and the Lord Jesus Christ as his bishop above him. Why didn’t Ignatius remind him that Rome had sole petrine succession and so its bishop was above him? We really mustn’t read into the fathers what we’d like them to be saying. Petrine succession as the sole perogative of the bishops of Rome did not exist in the early Church. It began its life as a claim by Victor in the calendar arguments and he was castigated by the other bishops for daring to claim superiorty for that reason, so even if he did have petrine succession is wasn’t considered of any particular importance - not in jurisdictional authority or spiritual authority.
All the arguments about Peter and the Rock are a red herring in this. It doesn’t matter what you think Christ meant if Peter can’t be shown to be** without a doubt**,
by clear teaching, an authority over the early Church by himself or his first successors in Rome and that has to start with proof that Peter was bishop in Rome to the exclusion of Paul and his ordained successors Linus and Anacletus and who is honoured by the Church for teaching that he was Peter’s equal.