I have written a number of articles addressing how ahistorical the official, dogmatic Roman Catholic teachings on the papacy truly are, including:
Perhaps one of the greatest historical events that refutes the teachings of Vatican I on the papacy and its primacy is that of the debate between Stephen, bishop of Rome, and Cyprian of Carthage (who believed that Peter was the rock of Matt 16:18, although he believed all bishops, not the singular bishop of Rome alone, sat on the “chair of Peter”). As Ivor Davidson wrote:
Cyprian may have sided with the winning party in Rome in the case of the Novatianist controversy, but his good relationships with Rome became severely strained during the episcopate of Lucius’s successor, Stephen, who was consecrated in May 254. Cyprian had accepted that regular believes who had compromised their faith might be restored, but what about the case of clergy? Not long after Stephen’s consecration, a clash occurred over the question of how to treat erring leaders.
Cyprian took it upon himself to advise Stephen that two Spanish bishops who had procured libelli to say that they had sacrificed must not be allowed to challenge the status of those who had subsequently been appointed in their stead. As far as Cyprian was concerned, the buying of certificates of compliance, though a lesser offense than actual sacrificing, was, in the case of leaders, a bar to restoration to office; the guilty could return only as penitent laymen. Stephen, on the other hand, judged that those who had originally been properly consecrated deserved to be restored if they were truly contrite. Cyprian and Stephen agreed at the authority of the church was vested in its bishops, but they differed as to what the implications of this authority were in practice. Could bishops directly remit the sins of delinquent clergy, or was a more protracted process of penitence required?
The fundamental issue on which the two leaders disagreed, though, was not discipline as such but baptism. Cyprian believed baptism was not valid unless it was administered by an official of the catholic community, for only such a person was qualified by the gifting of the Spirit to perform the rite. This meant that baptisms carried out by schismatics were by definition invalid; those who administered them were severed from the one Spirit-anointed body of Christ and were thus incapable of communicating the gifts of the Spirit to the candidates. For Stephen, however, the status of the minister was irrelevant; what mattered was the faith of the convert and the basic regularity of the process—it must be done in water and into the triune name.
Cyprian’s position was firmly grounded in the tradition of the North African church, which he consciously sought to follow. There it was simply assumed that the individuals who had been baptized by anyone other than catholic clergy had not genuinely been baptized at all and so were subject to the usual process of preparation and initiation required of all converts. Because the earlier rite was formally invalid, this process was not a rebaptism but a first real baptism. Baptisms performed by Novatianists were no better than those carried out by heretics, despite the fact that the Novatianists baptized into the triune name.
Cyprian had strong support for his argument not only in North Africa but elsewhere. In Cappadocia, Firmilian, bishop of Caesarea, had followed a similar practice with converts from Montantism and had been supported in it by his Asian colleagues. In Stephen’s view, however, all that was necessary when people came into the catholic community out of a schismatic or heretical context was that hands should be laid upon them, and the Spirit would be conveyed to them through that process. It had been the usual practice in Rome over many years for penitents to be received not by baptism but by the laying-on of hands. If Cyprian and his allies followed one established convention, Stephen could appeal to another.
The rift was serious. Stephen denounced Cyprian in very severe terms as a “false Christ,” refused to grant an audience to a delegation of North African churchmen, and threatened to excommunicate those in North Africa and Asia Minor who followed Cyprian’s teaching. Cyprian, for his part, convened a gathering of North African clergy in September 256 in which he consolidated support for his position and dismissed the legitimacy of Stephen’s attempt to impose his will on the other churches. Cyprian maintained that no bishop was in principle higher than any other, and no good argument could be adduced in favour of the spiritual primacy of the see of Rome. (It was perhaps at this stage that his original language in On the Unity of the Catholic Church was altered.) Confronted with a deep division between Rome and other churches, Cyprian’s foundation doctrine of the unanimity of bishops was in jeopardy; his way of defending it was to argue that all bishops were equal, and each was responsible to God alone. (Ivor J. Davidson, The Birth of the Church, volume 1: From Jesus to Constantine AD 30-312 [Oxford: Monarch Books, 2005], 330-31)
As another source of patristic scholarship noted:
Such an event is no endorsement of the dogmatic teachings promulgated by Vatican I; indeed, this debate, and the writings and practice of Cyprian reveal that he held an opinion directly opposing that of the dogmatic teachings of modern Catholicism, showing that, when the papacy is examined at the bar of history, as with many of Rome’s other dogmas (e.g., the Mass; the Marian dogmas), is found to be wanting.
[S]etting himself against the position of Stephen I (254-257), concerning the validity of baptism administered by heretics, Cyprian made it known that in his view the primacy of Peter did not extend to his successors. He even explicitly rejected the Roman claims that Stephen seems to have established upon Mt 16, while emphasizing the responsibility of the entire episcopal college for the unity of the church (Ep. 68,3). (Basil Studer, ‘Encyclopedia of Ancient Christianity’ 3:48-49)
Such an event is no endorsement of the dogmatic teachings promulgated by Vatican I; indeed, this debate, and the writings and practice of Cyprian reveal that he held an opinion directly opposing that of the dogmatic teachings of modern Catholicism, showing that, when the papacy is examined at the bar of history, as with many of Rome’s other dogmas (e.g., the Mass; the Marian dogmas), is found to be wanting.