"But didn’t Peter refer to himself as a “fellow elder” and not as “pope” in 1 Peter 5:1? Yes, but in this passage Peter is demonstrating humility that he is encouraging other priests to practice. He wrote, “Clothe yourselves, all of you, with humility toward one another” (5:5), so exalting his status would have contradicted his message. Besides, St. Paul often referred to himself as a mere deacon (see 1 Cor. 3:5, 2 Cor. 11:23) and even said he was “the very least of all the saints” (Eph. 3:8)—but that did not take away from his authority as an apostle. Likewise, Peter’s description of himself as an elder does not take away from his authority as being “first” among the apostles (Matt 10:2)."
The above argument rests on a few questionable presuppositions: 1.) Peter described himself in the humblest of terms in order that he set a good moral example and not that he knew nothing in regards to having been bestowed papal authority, and 2.) Peter was addressing members of an ordained ministerial priesthood. There is no evidence for either claim. Even granting that the apostle is setting forth a model for other pastors to emulate, 1 Peter 5:1 weakens the Roman Catholic case for Peter being first pope because it indicates that he put himself on par with other elders in the church. He never indicates being in a superior position of authority. He never distinguished himself from other elders in the church.
"In regard to the authority of the Bishop of Rome as Peter’s successor, in the first century Clement of Rome (the fourth pope) intervened in a dispute in the Church of Corinth. He warned those who disobeyed him that they would “involve themselves in transgression and in no small danger,” thus demonstrating his authority over non-Roman Christians."
Churches established by Peter and Paul were led by pluralities of elders called bishops (Acts 20:17, 28; 1 Peter 5:1-4). Every man in that position wielded that title without exception. There were originally two classes of leadership: bishops and deacons. Clement used the terms elder and bishop synonymously. The New World Encyclopedia has this excerpt which says:
"The First Epistle of Clement does not claim internally to be written by Clement, but by an anonymous person acting on behalf of the Roman church to the church at Corinth...It may be that the writer is himself a presbyter or one of several bishops (overseers) who also acted as the church's secretary. If he were the reigning bishop, it seems likely that he would refer to himself as such or signed the letter by name."
"St. Ignatius of Antioch referred to the Roman Church as the one that teaches other churches and “presides in love” over them. In fact, the writings of Pope Clement (A.D. 92-99) and Pope Soter (A.D. 167-174) were so popular that they were read in the Church alongside Scripture (Eusebius, Church History 4:23:9)."
The above presented information shows us, not that Rome held a position of primacy, but it was honored amongst other churches. Eastern Orthodox commentator Andrew Stephen Damick notes the following regarding the use of Ignatius to support papal authority:
"…the modern Roman Catholic vision of Church unity being defined by subjection to a worldwide bishop in Rome is not found in Ignatius’s writings. We saw how he described his friend Polycarp, the bishop of Smyrna as “one who has God the Father and the Lord Jesus Christ as his bishop” (To Polycarp, Salutation). He does not say that Polycarp has the bishop of Rome for his bishop nor even a regional Asian primate (i.e., a senior bishop in his area). Being a bishop, Polycarp’s bishop is God. With all that Ignatius has to say about the episcopacy and especially about unity, he had the perfect opportunity to insist on a worldwide pontificate for Rome’s bishop. Rome was certainly on his mind, since he was traveling there to be martyred as Peter and Paul had been before him. Yet in his six letters addressed to churches, it is only his letter to Rome in which he does not even mention their bishop (who was probably either St. Evaristus or St. Alexander I). In the other five letters to churches, the bishop is mentioned, and in three of them, the bishop is mentioned by name. When writing to the Roman Christians, he does mention Peter, but equally with Paul as both are apostles who could give them “orders,” while Ignatius himself would never presume to do that (Romans 4:3). In Ignatius’s writings, there is never any special role given to the Roman bishop or the Roman church, nor even to the Apostle Peter. And when he writes to Rome, he does not ask the Roman bishop to send a bishop to Antioch to replace him. Rather, he makes that request of Polycarp and his church in Smyrna (To Polycarp 7:2)."
"In A.D. 190, Pope St. Victor I excommunicated an entire region of churches for refusing to celebrate Easter on its proper date. While St. Irenaeus thought this was not prudent, neither he nor anyone else denied that Victor had the authority to do this. Indeed, Irenaeus said, “it is a matter of necessity that every Church should agree with this Church [Rome] on account of its preeminent authority” (Against Heresies, 3.3.2)."
The West and certain Eastern churches claimed to have the correct date of Easter that was delivered from the apostles. If this episode of contradictory church tradition proves anything at all, it would only be that it is unreliable as a source of dogma. What we are left with is Scripture as our guide in building our theology. Irenaeus did not say that churches should submit to Rome due to it being higher in authority, but come together as that church was reputed for being doctrinally orthodox. Consider this introductory excerpt from Philip Schaaf on the translation of Irenaeus's Against Heresies:
"After the text has been settled, according to the best judgment which can be formed, the work of translation remains; and that is, in this case, a matter of no small difficulty. Irenæus, even in the original Greek, is often a very obscure writer. At times he expresses himself with remarkable clearness and terseness; but, upon the whole, his style is very involved and prolix. And the Latin version adds to these difficulties of the original, by being itself of the most barbarous character. In fact, it is often necessary to make a conjectural re-translation of it into Greek, in order to obtain some inkling of what the author wrote. Dodwell supposes this Latin version to have been made about the end of the fourth century; but as Tertullian seems to have used it, we must rather place it in the beginning of the third. Its author is unknown, but he was certainly little qualified for his task. We have endeavoured to give as close and accurate a translation of the work as possible, but there are not a few passages in which a guess can only be made as to the probable meaning."
Consider translator footnote 3313 from that same version of Irenaeus's Against Heresies:
"The Latin text of this difficult but important clause is, “Ad hanc enim ecclesiam propter potiorem principalitatem necesse est omnem convenire ecclesiam.” Both the text and meaning have here given rise to much discussion. It is impossible to say with certainty of what words in the Greek original “potiorem principalitatem” may be the translation. We are far from sure that the rendering given above is correct, but we have been unable to think of anything better. [A most extraordinary confession. It would be hard to find a worse; but take the following from a candid Roman Catholic, which is better and more literal: “For to this Church, on account of more potent principality, it is necessary that every Church (that is, those who are on every side faithful) resort; in which Church ever, by those who are on every side, has been preserved that tradition which is from the apostles.” (Berington and Kirk, vol. i. p. 252.) Here it is obvious that the faith was kept at Rome, by those who resort there from all quarters. She was a mirror of the Catholic World, owing here orthodoxy to them; not the Sun, dispensing her own light to others, but the glass bringing their rays into a focus. See note at end of book iii.] A discussion of the subject may be in chap. xii. of Dr. Wordsworth’s St. Hippolytus and the Church of Rome."
"Some people object that if Peter and his successors had special authority, why didn’t Christ say so when the apostles argued about “who was the greatest” (Luke 22:24)? The reason is that Christ did not want to contribute to their misunderstanding that one of them would be a privileged king. Jesus did say, however, that among the apostles there would be a “greatest” who would rule as a humble servant (Luke 22:26). That’s why since the sixth century popes have called themselves servus servorum Dei, or “servant of the servants of God.”
If Peter had an exalted position over the other apostles, then why did Jesus Christ not clear up confusion on this matter by pointing to him? He could have put that matter to rest easily. Trent Horn offers us nothing but smoke and mirrors. The pope with his kingly attire and multitudes who bow down before him in adoration is not in the slightest a "humble servant." Jesus was not referring to any specific individual in Luke 22:26 but offering a general description of anyone who does service for the Kingdom of God.
"Pope Gregory I used the title in his dispute with the Patriarch of Constantinople John the Faster, who called himself the “Universal Bishop.” Gregory didn’t deny that one bishop had primacy over all the others, since in his twelfth epistle Gregory explcitly says Constaninople was subject to the authority of the pope. Instead, he denied that the pope was the bishop of every individual territory, since this would rob his brother bishops of their legitimate authority, even though they were still subject to him as Peter’s successor."
That is absolutely untrue. Gregory emphatically denounced the title of universal bishop. He thought that such should be reserved for no one. The following excerpt has been taken from the New Advent Catholic Encyclopedia as an example:
"a proud and profane title ... I have however taken care to admonish earnestly the same my brother and fellow-bishop that, if he desires to have peace and concord with all, he must refrain from the appellation of a foolish title. ... the appellation of a frivolous name. But I beseech your imperial Piety to consider that some frivolous things are very harmless, and others exceedingly harmful. Is it not the case that, when Antichrist comes and calls himself God, it will be very frivolous, and yet exceedingly pernicious? If we regard the quantity of the language used, there are but a few syllables; but if the weight of the wrong, there is universal disaster. Now I confidently say that whosoever calls himself, or desires to be called, Universal Priest, is in his elation the precursor of Antichrist, because he proudly puts himself above all others." (Gregory the Great, Book VII, Epistle XXXIII)