I’m very sorry my little book has caused you some uneasiness, but I don’t really think you need be concerned. You might find it helpful to look at the opening chapter of my larger full-scale history of the Popes, Saints and Sinners, which treats the issues you raise in more detail.

But if I can address your worries briefly: two issues seem clear enough: the new testament attributes a distinctive and primary role to the apostle Peter, which he received from Christ himself: and from the earliest point at which there is evidence, it was assumed in the early Christian world that in some sense or other, the apostolic authority of BOTH Peter and Paul inhered in the church at Rome: so by the third and probably by the late second century, churches elsewhere in the mediterranean were referring problems and seeking guidance from the Church at Rome, and deferring (if not absolutely!) to its authority. By the third century, that assumption of apostolic authority had become the subject of overt theological reflection and debate, and at that point bible texts, including “Thou art Peter....” get cited in its favour. The fact that those texts aren’t cited in the way familiar to modern RCs like you and me till then, doesn’t , so far as I can see, bring into question the validity of the Roman Church’s claims – after all, the doctrine of the Divinity of the Holy Spirit didn’t get defined till the 5th century , but we don’t for that reason doubt the truth of the doctrine. Theological reflection takes time to articulate the faith the Church had been practising before anyone got round to working out how you would justify or explain it.

As for the succession of popes, I think the key thing to grasp is that the inheritor of the Apostolic charism at Rome was the CHURCH at Rome: the early documents are all clear that it is the community as a whole which carries the weight of apostolic authority, though in practice that was inevitably exercised by and expressed through the leaders, in a hierarchic sense, of the Roman church. There must always have been some kind of leadership and oversight (which is what the word “bishop” means) after the age of the apostles, but for historical and sociological and ethnic reasons there were always a range of Christian communities at Rome, so that oversight, or episcopacy, seems to have been exercised at first through a number of presbyters, what we would now call a College, and only gradually focussed as everywhere else in the person of a single “monarchic” bishop, a process which seems to have been completed in Rome by about 160 or so, and which was probably slower to settle there than in many other christian communities, because Rome was so vast a place, and the churches reflected the social reality of the city, so full of ethnic and linguistic diversity as the greatest and most cosmopolitan city in the ancient world . I myself see no problem about taking that process of settlement, and the establishment of a single unitary authority over the various churches in the city – as a providential evolution, in continuity with the ministry of the Apostles, and I can’t see myself that this prevents us seeing the popes as the rightful inheritors of the Apostolic ministry. But the fact that it was the community, the Church of Rome, in the first instance, and only secondarily the individual bishops of that Church of Rome, who were understood as inheriting the Apostolic role, is a salutary check on some absolutist understandings of what the papacy is and how it should be exercised. You might like to look at the very fine (and short!) book on all this, just titled The Bishop of Rome, by the distinguished Dominican theologian, Jean Tillard (now, sadly, dead) .

I hope some of that is helpful to you
All good wishes
Eamon Duffy

Since you got Mr. Duffy's reply, this may or may not be useful, but I picked up A Book of Essays by Monsignor Benson from the school library today, and in his essay "Infallibility and Tradition" he touches upon this subject in a most satisfactory way, though it isn't the focus of the whole essay.

However, I haven't the slightest idea how easy it may be to find it outside dusty academic libraries, and Mr. Duffy's explanation is similar to the late Monsignor's, so...