RIGHT! There were TWO Catholic Churches that had Rome as its center! How silly of me!
This information you have is not bad, but it is incomplete and biased. CCEL is a fairly good site. But, for example:
"The same Irenaeus frankly opposed the Roman bishop Victor."
Your site doesn't say why, now, does it? Nor does it say that Irenaeus COMPLIED with the Bishop of Rome, does it? Pope Victor was a bit "authoritative" regarding the determinination of the date for Easter. Victor wanted it according to the date in the West, vs. those in the East. He threatened those who did not comply with excommunication. St. Irenaeus thought this went too far, that cooler heads should prevail. But he never questioned Victors RIGHT to do just that! By typing the above, this Protestant site covers up the fact that this complaint does not take away anything from the Papacy, but ADDS to its seen role during 180 AD!
Tertullian, though he continued essentially orthodox, contested various points with the catholic church from his later Montanistic position
Tertullian, unfortunately, became a heretic. It wasn't anything to do with the Pope's authority, but that Tertullian thought that church discipline should be more strict. The Church decided to weigh in on the side of leniency. Is it surprising that a heretic would later contend with the Church???
St. Cyprian, with whom biblical and catholic were almost interchangeable terms, protested earnestly against the Roman theory of the validity of heretical baptism
You need to learn more about history. Cyprian wanted all of those who recanted the faith during persecution to be either not allowed back into the Church, OR those who were in heretical sects, to be re-baptized by the Catholic Church. Pope Stephen denied this need to rebaptize. He utilized Scripture and Tradition to defend his stand. Cyprian was wrong, and later admitted it. This only further enhances the necessity of the Papacy in maintaining the teachings of the Apostolic Church. Such examples as this are scattered THROUGHOUT the Church's history.
Regards
The defense of tradition was based on its adherence to scripture.
To estimate the weight of this argument, we must remember that these fathers still stood comparatively very near the apostolic age, and that the succession of bishops in the oldest churches could be demonstrated by the living memory of two or three generations. Irenaeus in fact, had been acquainted in his youth with Polycarp, a disciple of St. John. But for this very reason we must guard against overrating this testimony, and employing it in behalf of traditions of later origin, not grounded in the scriptures.
The Roman Catholic Church of today is from the 4th century.
No one denies you can find germs (an apt term) of it's development in the writings of the various church 'fathers'.
Where you cannot find it is the Scriptures.
Regarding the history of the Papacy,
There were five principal Sees in the early church. They were Jerusalem, Alexandria, Antioch, Rome, and Constantinople. Each was presided over by a Patriarch or a Pope. The title 'pope' was originally not specific to the bishop of Rome, but was applicable to all bishops or pastors, and sometimes was even used for teachers. Each of these five Sees had jurisdiction within their geographic area. The Church government was conducted through regional councils or synods. These councils would write canons that were the law within that jurisdiction. Often one regional council would receive and adopt canons of other regional councils. More detail on early canon law is found here. Additionally, there were ecumenical councils that were attended by bishops from the entire Church.
The bishop of Rome, because he was seated in the imperial city, was accorded a primacy of honor in councils. This conferred on him things like a more honorable seat and a higher place in the roster of speakers, but did not impute to him any authority, for the authority was in the Council rather than in any individual. Later, when the empire divided into the Eastern and Western halves, the See of Constantinople, known as the New Rome, was granted an equal dignity with Old Rome, though ranking second after it.
Stephen I, bishop of Rome, was the first on record to attempt to exert authority over other churches on the basis of succession from Peter. He attempted by letters to overrule the decision of a council of African bishops concerning the baptism of heretics. In response, the Africans held a larger council of 87 bishops which upheld the previous council and rejected Stephen's decrees. This was the Seventh Council of Carthage in 258.
It was in the latter half of the eighth century that there appeared a document purported to be a legal title granted by the emperor Constantine, in the fourth century, to Sylvester bishop of Rome. It granted to the Roman bishop, among other things, " supremacy... over the four chief seats Antioch, Alexandria, Constantinople and Jerusalem, as also over all the churches of God in the whole world." Before this document the papacy could not effectively assert itself, because the Church had only the Scriptures and the documents of the various councilsnone of which established or supported any such office as the papacy. But here emerged a forgery, that was received everywhere as genuine, that exalted the Roman See not only above the other four principal Sees, but over the entire Church.
The Donation of Constantine provided the bishop of Rome with what appeared to be a legal claim to everything he had sought, but to which he previously had no right. He was now 'rightfully' acknowledged to be the sole and supreme spiritual ruler over the entire Church, as well as the temporal ruler over a large swath of Italy that became known as the Papal States. The Donatio was proven to be a forgery by Lorenzo Valla in 1440 in his Declamatio. But, by that time the structure of the papacy was set in place, and its adherents were well under its control, and largely either unable or unwilling to forsake it.
Not long after the Donation, there appeared in the late eighth or in the ninth century another forgery, or rather, collection of forgeries, which was widely accepted as genuine, and which also served to greatly strengthen the power and prestige of the papacy. The False Decretals were a collection of forged letters or 'decretals' purporting to have been written by earlier bishops of Rome. These decretals made vast and far-reaching claims of power and authority for the bishop of Rome that were made to appear as though they had long been established in antiquity.
Phillip Schaff writes of these Decretals, ¶ Fictitious documents, canons, and decretals were nothing new; but the Pseudo-Isidorian collection is the most colossal and effective fraud known in the history of ecclesiastical literature. History of the Christian Church, by Phillip Schaff, Volume IV, Chapter IV, § 60
It was by means of these forged documents, along with others of similar character, that the papacy was provided with a pretended apostolic origin, lineage from Peter, and headship and authority over Christ's Church as well as over the kings of the earth.
http://jmgainor.homestead.com/files/PU/OP/OP.htm
As for learning history, the only history that a Roman Catholic apologist knows is the one that the RCC had made up.
'regards'