The apostle Peter went to Rome, died and was buried there. Or not, depending on whom you talk to. In any event, the people who went on to invent the Papacy thought that Peter did die in Rome, so that’s what is most relevant at the moment. He was known the ‘Rock’ of the Church, the earliest known reference to professional wrestling in Western Europe. Rome was the centre of the Roman Empire and therefore probably the best place to try to convince the Romans to stop killing your mates because they believed in one god, not one for every day of the week, every event and every place; that’s what saints are for. But the Church in Jerusalem probably held precedence over Rome because of its connection to the person they thought to be most important, Jesus, not the Emperors, of which they may have been more than one depending on the whims of the army. Over time Antioch, Alexandria and Constantinople all rose in importance, the last one particularly as the seat of the Empire moved there under Constantine, but there was no real organised Church until the second century. These five Churches held councils, organised picnics, and chastised heretics and scolded schismatics. Clearly this disunity and lack of organisation would not appeal to a people fond of building roads with no bends, rivers with no bends and empires with no bends. They were not a bendy people. They probably never had a law that said it was okay to steal food for a pregnant woman because she craved it, which the early Irish did because they were more enlightened about women’s issues. A woman could even divorce her husband under Irish law if he was too fat or old to have sex. Anyway, the Emperor Constantine decided he didn’t like the idea of a myriad different doctrines and discussions and arguments and bibles and such. So he gathered all the bishops together in the city so good he named it after himself (actually he called it Nova Roma, but everyone else thought Constantinople was catchier) and told them to come up with one Church or else he’d introduce them to some pointy bits of steel, or maybe some playful felines.
What with Nova Roma being the new seat of the Empire old Rome was suddenly not the place to be on Friday nights. So the bishops of Nova Roma thought that they should be the primary Church in the land, but so did Rome since they held the seat of the Empire first and for far longer and sure they were ‘old’ but that doesn’t mean they still couldn’t be a useful participant in society and shouldn’t be ignored just because they are kind of forgetful and leave the lights on from time to time…. For the sake of convenience the Empire was divided in twain and a short while later a bunch of Germans decided to move in to the Western half. You’d imagine all the new barbarian kingdoms would bow to Rome and the East would follow Constantinople, but they were barbarians and didn’t know that’s how things worked and so made a mess of the very neat and unbendy empire. The men who would be Pope had to contend with the very independent Visigoths, Franks and Germans who generally didn’t like being to what to do at the best of times. The best example of that is of course when a Roman guard said ‘No, you can’t come in, sure aren’t ye fine where ye are?’ The Churches of North Africa and Spain considered Rome to be an intellectual backwater and so largely ignored it for a long time but then the Umayyad came to show them how wrong they were. On their way to Spain they also cut off Antioch, Alexandria and Jerusalem from the rest of Christendom until some men encased in steel decided they wanted it back. This left Constantinople and Rome as top dogs of the Christian world, or so they liked to believe at an any rate. Rome made a concentrated effort to become dominant in the West, often in collusion with powerful kings, like Charlemagne. Conveniently named people like Gregory the Great instilled strange notions like morality on the clergy at large because the reality was in the Middle Ages that a substantial amount of clerical appointments were due to politics and money and who you knew rather than how pious you were. Monks, abbots and bishops were often expected to not only pray for but fight in the king’s army, which one would imagine ran contrary to the whole Christian experiment. For a time the Popes lived in France under the control of the king, but eventually they moved back to Rome, because let’s face it Rome is a wicked cool city, where they ruled the Papal States as a secular prince, expanding their domains through conquest and diplomacy, which might seem strange to modern eyes but was the done thing in those days. There were Popes and Anti-Popes, a special type of Pope made in a particle accelerator at CERN, and splits and schisms and then a man nailed a note to a door which caused more wars. And now the priest faces the congregation and doesn’t speak in Latin anymore, which is useful because neither does anyone else.
The evolution of the papacy from being one of the many leaders of Christianity to being the dominant voice in Western Christendom is a long a complex history involving the interplay between religion and politics, personal gain and true piety. This is over one thousand years of history in less than one thousand words so clearly the reality is far more intricate with many nuances.