Many emperors of Rome coming after Nero kept up the brutal killings of Catholics. As this killing was going on, Romans are being surprised that Christians easily, willingly submit themselves to death rather than worship idols and offer incense to them. So instead of the killings destroy Christians, it emboldened them as many more Romans converted to Christianity. Not the use of the words Christianity and Catholicism interchangeably.
As more Romans continue to adopt Christianity in large numbers, Rome found itself suppressing riots and insurrections throughout the empire as more people reject the method of killing Christians and many supporting that. So riots were the order of the day and Rome was spending resources suppressing these riots, including trying to suppress band of brutal runaway slaves made up of gladiators.
The emperor ruling at this time was Constantine, a man in support of stopping the killing of Christians. He had other more ingenious plans on how to finish off Christians without the constant bloodletting. He was planning to re-educate them forcefully into the Roman culture.
As Rome was suppressing riots, it was also facing a war with Germanic tribes who plunder the vestiges of Rome spreading fear and terror among the Roman suburbs. So, Rome wanted to invade Gaul, today’s Germany to put a final stop to these murderous raids. So as the war preparation was on, the head of the Catholic Church who have been in hiding somewhere in the catacombs, the Roman underground went to the emperor knowing that the emperor will either listen to him or he will die. So he gambled.
This pope told Constantine that he should make the crucifix his standard in the coming war promising a sure victory. Constantine was intrigued and he agreed. And so he went on to win the war decimating the Germanic tribes taking thousands of them prisoners.
When he returned to war, he converted to Catholicism and changed the law making Christianity to official religion of the whole of the empire. Pagans were on the defensive but what is written is written. This means that Catholicism permeated all aspects of life of Rome. The emperor have an oversight as to who is appointed Bishop or the location of any Church.
So the Christians triumphed over Rome and the Pope was given a house and he started to rule over Christianity in peace. Thus what we now call Roman Catholicism was born. It is also a testimony that it was only in Rome that existed the most organized center of Christianity, where St. Peter ruled from, albeit in secret.