There were multiple schools of thought in the pre-schism Church, on multiple subjects.
For instance: the emphasis on Jesus having two natures was the Constantinopolitan/Antiochian school of Christology. It first degenerated into Nestorianism, but afterward became the main and universal doctrine of the Church.
The emphasis on Jesus's two natures being united was the Alexandrian school of thought. It first degenerated into monophysitism (Eutychianism), but afterward tended toward miaphysitism, which became the main doctrine of the Oriental Orthodox communion, while a Chalcedonian perspective on them would be anything from "they're straight up Eutychians" to "they're just like us but they're stubborn in mistakenly anathematizing dyophysitism".
Another example: Biblical exegesis. The Alexandria school is to have an allegorical, mystic interpretation. The Antiochian school is to have a strict, literalist interpretation.
There were different schools of thought regarding the Papacy too. I observe three schools of thought:
- The Roman school. The Pope is the successor of Peter, in such a way that he inherits the same position, prerogatives, and powers - supreme doctrinal and pastoral authority. He is the Vicar of Christ, the sole true guardian of orthodoxy, and he indeed is, mystically, Peter. St Jerome's views express it best: the sentence "no salvation outside the Church" only really applies to the Church of Rome, and any other Church only derives its orthodoxy from Rome. Note that this exalted view of the Pope was bolstered by how the Church of Rome was the only significant Church of apostolic origins in the West.
- The African school. The Pope is the -main- successor of Peter. Peter's powers immediately extended to the other apostles, and through them to all bishops equally. The Church of Rome is special in that, among the Churches, it functions like Peter did (as the proof of unity and the source of sacramentality) but every bishop has strictly the same powers.
- The Byzantine school. The Pope is the successor of Peter, and indeed plays the role of Peter among the communion of bishops today. This means that if the bishops possess power, it's thanks to him, and he must play the role of Peter, having the highest doctrinal and pastoral authority in the Church. However, this never extended to an idea of true infallibility, but rather a strong protective grace inherited from being founded by Peter and Paul. With the establishment of the Pentarchy, this view became even stronger - the Church was seen as a "confederate" of 5 ruling Churches, with the "elder sister" being Rome, which holds a special prerogative and holds the keys of heaven for everyone else. Indeed, the view of Peter as choir leader of the apostles became current, and Rome was the choir leader of the Churches.
The Roman view, obviously, evolved into the current Roman Catholic view. The African and Byzantine views are both found, to varying degrees, in the Orthodox communion today.
What is Rome's error then? It is to have taken Western theology to be necessarily the normative and universal theology, without respect for the other Churches. The problem of the filioque, of papal supremacy, of Purgatory, etc. become not that they are heretical new innovations (they are not) but that they shouldn't be considered dogma, without further discussion, simply because they are cherished of Western Christendom. What was a choir led by Rome, became a solo.
Incidentally, I believe that the Byzantine theological tradition reflects best the biblical and apostolic truth. So, of course, I would say Rome has badly hurt itself by shunning it as it did (and later theologians misinterpreting Greek patristics to support their strictly Latin theology didn't help).
Who the hell told you that?
For what it's worth, Pope Leo III did not reject the filioque's theology, but rejected the idea that he had superior authority to an ecumenical council.
