Jesus said: "You will know them by their fruit." Matthew 7:16
In the fruit of correct doctrine, Rome has consistently passed the test for 2000 years, proving that the promise of John 16:13, "He will lead you into all truth" rests upon the bishop of Rome.
Consider the major heresies that have plagued the Church, and how Rome fared compared to other ancient sees:
One of the earliest proponents of adoptionism, Theodotus of Byzantium, was excommunicated for his heresy by Pope Victor I in the 2nd Century. In contrast, the bishop of Antioch, Paul of Samosata, ascribed to adoptionist beliefs as late as AD 260-268.
The most famous proponent of modalism, Sabellius, was excommunicated by Pope Callixtus I in AD 220.
The Council of Nicea in AD 325, which was presided over by a westerner loyal to Rome, Hosius, did not end the Arian controversies in the eastern part of the church. By AD 338, a committed Arian, Eusebius of Nicomedia, was made bishop of Constantinople. Paul I of Constantinople, who held to Nicene orthodoxy, was only allowed to return to the bishopric of Constantinople under the threat of force by the western Emperor Constans at Rome. After the death of Constans, Constantinople would continue to have Arian or semi-Arian bishops until 380 when a westerner, Emperor Theodosius I, took the throne of the entire empire and outlawed Arianism and semi-Arianism. In doing so, Theodosius explicitly declared that the entire Church must follow the apostolic tradition of Saint Peter that had been preserved at Rome.
Likewise, Antioch was led by Arian or semi-Arian bishops prior to Theodosius, such as Stephanus I, Leontius the Eunuch, and Eudoxius. Arianism and semi-Arianism in Antioch led to the Meletian Schism in 362, in which Arian, semi-Arian and orthodox bishops claimed the see.
In Alexandria, Pope Athanasius I held fast to Nicene orthodoxy but was deposed by the Eastern Emperor and replaced with the Arian Gregory of Cappadocia from 339-346. During his exile, Athanasius fled to Rome, where he was protected by Popes Julius and Liberius, who held fast to the orthodox Nicene Creed of 325. Pope Liberius was ruthlessly persecuted by western Emperor Constansius II for his support of Athanasius and orthodox Nicene Christianity. While some claim that Liberius was coerced into assenting to Arianism by Emperor Constantius, it is undisputed that Pope Liberius remained steadfastly orthodox from his return from exile until the end of his papacy.
No sooner had the eastern sees accepted Nicene orthodoxy in AD 381 than they were swept up in the new heresy of Nestorius, bishop of Constantinople from 385-431, who taught that there were two persons in the Incarnate Christ, one divine and one human, and therefore that Mary was not the Mother of God. Nestorius was rightly condemned by Pope Cyril of Alexandria and Pope Celestine I of Rome. In contrast, Patriarch John I of Antioch supported Nestorius and called a council to condemn Cyril.
Alexandria, which had remained orthodox to this point, succumbed to the heresy of Monophysitism under Patriarch Dioscorus, who taught that Jesus has one nature rather than two distinct Divine and human natures. While Dioscorus prevailed over the bishops at the Second Council of Ephesus in 449, Pope Leo I of Rome remained steadfastly orthodox that Jesus has two natures, Divine and human, and Pope Leo I's doctrine prevailed at the Council of Chalcedon in 451. Dioscorus’ successors in Alexandria never accepted the orthodox doctrine of Pope Leo I and the Council of Chalcedon.
For 200 years the orthodox doctrine of Chalcedon met with great opposition throughout the eastern church, while Rome remained steadfastly orthodox. Patriarch Sergius of Constantinople attempted to unify the eastern church with the compromise that Jesus has two natures but, alternately, a single energy or a single will. Sergius wrote to Pope Honorius I in the 630s, and although Pope Honorius I appeared to give his consent in a letter to Sergius, Pope Honorius I made it clear that he considered the problem one of terminology, not theology. By the time Sergius’ heretical ideas were widely disseminated by Emperor Heraclius in the publication Ecthesis, Pope Honorius I had died and his successor Pope Severinus immediately condemned the monothelite heresy, as have all successor Roman Pontiffs. Thus, while opponents of Rome have attempted to use Pope Honorius I as an example of papal heresy, the only evidence against him is a single a letter to the Patriarch of Constantinople in response to an initial inquiry from the Byzantine Patriarch, and as Maximus the Confessor states, it is clear that Pope Honorius I’s opposition to the idea of two wills was based on the interpretation of two wills as “two contrary wills.”
When the Byzantine Emperors fell into iconoclasm in the 8th Century, they were steadfastly opposed by Pope Zachary and Pope Gregory III in Rome, whose orthodox views prevailed at the Seventh Ecumenical Council.
Thus, throughout all the great doctrinal disputes of the Church in the First Millennium, Rome upheld correct orthodox doctrine each and every time. Saint Irenaeus was therefore correct when he wrote, “it is a matter of necessity that every Church should agree with this Church, on account of its preeminent authority. ”newadvent.org/fathers/0103303.htm
Rome has always born good fruit on matters of doctrine, and all Christians should therefore follow Jesus' command and follow the church at Rome.