There's no two ways about it: disagreements are just not edifying. I have to force myself to write such a post as this, even to reply to such a kind soul as Japhy. And I have to wonder how much good is accomplished. If any good is accomplished, it would have to be this: to make a clear statement about exactly what the disagreement is, and what causes it, and what might repair it. Otherwise it becomes more a matter of rehearsing differences (or worse, rehearsing grievances) which accomplishes nothing good. I might even hope to offer reasons why the entrenched positions should be open to reconsideration.
Writing this, I know full well that the most likely reaction is -- must be -- that it will be dismissed out of hand based on entrenched positions that are not open to reconsideration, that it will be read not in the spirit of seeing whether it has anything useful to say or any insight or any gain for moving forward, but in the spirit of finding how it is -- how it must be -- wrong. That is the nature of such a division. That is one of the saddest parts of our divisions: that two followers of Christ could be robbed of their ability to see each other, hear each other, listen to each other, by the assumption that the other simply must be wrong and therefore simply must be dismissed, simply must have nothing to contribute to a conversation on that particular subject. In that scenario, the conversation really has no right to take place: there is no basis for disagreement, only an error that needs correcting. And so a conversation does not take place.
With our current example of the bishop of Rome as pope, I think the most useful place I can start is here: What is a pope? A Roman Catholic friend of mine once patiently explained that the pope is the fellow who speaks for the whole church. He is the bishop of the foremost see of the church, the one with primacy. He's only considered infallible under certain very limited circumstances: when issuing decrees ex cathedra for the whole church with the consensus of the whole church. Here he serves as the voice of the church, the unifying focal point of the church. Insofar as he speaks for the whole church united (one, holy, catholic, and apostolic), he can be assumed to have reached the right decision. I hope I've understood that correctly.
So if that is the theory, what is the historical reality? Where do we first see such a thing? The council of Jerusalem (Acts 15) took place early in the church's history. There was yet no bishop of Rome; the decisions for the whole church were made from Jerusalem. Still, there was a leader from the beginning. There is one who issues a decree ex cathedra, one who speaks from the primary see of the church of that day, one who is bishop of that primary see, one who gives voice to the decree of the church with the consensus of the church. That person is James. All the arguments in the world that when Jesus said "Feed my sheep" he meant "Have authority over the whole church" carry no weight when there is no sign that the person to whom it was addressed understood it that way, no sign that the person who recorded the conversation for posterity understood it that way.
Speaking for the whole church. The church has not been whole in any meaningful sense since Chalcedon. Before that, the breaches had not affected the major centers of apostolic Christendom. To get the feel for what happened at Chalcedon, consider this. Think of the little breaches before Chalcedon as "what would happen to the U.N. without Luxembourg, Liechtenstein, and Lithuania". Think of Chalcedon as "what would happen to the U.N. if China, India, Russia, and the U.S. would no longer sit at the same table." Nobody has spoken for the whole church since Chalcedon; the church has not been whole since then, and more than just crackpot heretics were swept away in that breach. There have been no valid decrees for the whole church since then because the whole apostolic church has not agreed on a decision since then. That breach broke fellowship with more than just oddballs who wanted to reinvent Christianity to suit their own preferences. That breach broke fellowship not between the apostolic church on one side and trackless, rootless heretics on the other, but pitted one apostolic church against another. The unity of the Christian church was broken, and nobody could claim to speak for the whole church because the church was not whole. Every voice was a partisan voice, the bishop of Rome against the bishop of Alexandria. Nobody can rightly judge a dispute in which he is a party. Rome eventually decided that Rome was infallible. Many Christians eventually decided that Rome, because she considered herself infallible, was therefore unreformable. I wouldn't go that far: almost anyone will realize they are fallible if they are humbled. I am not sure how far Rome would have to be humbled before she acknowledged that she was fallible.
From my point of view, the most necessary change is for Rome to become humble as Peter was, to admit mistakes publicly and accept correction graciously as Peter did, to know that repentance and humility are at least as necessary in the church body as they are in the individual members. See, here's the thing: I know a lot of Protestants who are tired of protesting. I know a lot of Protestants who wish Rome was what Rome claimed to be, who would dearly love to see the church re-united. But for most of us, we know too well which teachings were late-added, which were changed, which build up Rome more than they build up Christ, which are not from the apostles, which amount to human teachings. We know Rome isn't infallible. But it is the idea of her own infallibility that Rome guards the most jealously of all her late-developed doctrines. It's a given in Roman Catholic circles that Rome has never been wrong, that the protests are entirely mistaken, that there is no reason whatsoever for Rome -- or any individual Christian affiliated with Rome -- to listen when another Christian calls for reform in Rome, because we cannot possibly have a point.
In order for there to be a change, enough Roman Catholics would have to privately within their own ranks allow it to become thinkable that Rome has become partisan rather than catholic, has acted on her own behalf instead of for the good of the whole, that humility is in order, that fallibility is possible, that repentance is a virtue for the church herself. As long as it is unthinkable that we have anything worthwhile to say in our protests, we will not be heard but dismissed out of hand. And every time one Christian dismisses another out of hand, a brick is added to the wall of separation between us.
So we each have to make our appeal for unity as best we know how. Some Roman Catholics honestly believe that Rome is infallible and that the best they can do is to proclaim that until all the "erring brothers" come home. Some Roman Catholics are not convinced that Rome is infallible but know it's a one-way ticket out the door to say so plainly, and have no wish to leave. Others are not convinced that Rome is infallible but are frightened that, if Rome isn't infallible, then nobody is infallible and they would not be sure what to believe. All I can ask is that we be human beings to each other, brothers and sisters in Christ. For anything more than that, I have to trust each one to go forward as best he knows how.