The first seven ecumenical councils were invoked by the emperor of Rome, their statutes decided upon by the bishops of the Christian world. Thus, I hope we can agree that the first seven ecumenical councils were the product of conciliarity. The organization and conduct of these councils is the groundwork for the operation of present Eastern Orthodoxy. We resent the efforts of any single bishop to impose his will upon the whole faith (as we see with our righteous opposition to the actions of the EP with regard to Ukraine). This, the contrast to conciliarity, is called ultramontanism.
The Great Schism highlights not only differences between "Greek East" and "Latin West" but also between conciliarity and ultramontanism, terms that would only really be used later in Roman Catholic history.
Personally, I wonder how anyone can ustify the ultramontanist position in light of the conduct of the first seven ecumenical councils, clearly conciliar efforts. It is this precise reason that many people, including myself, have decided to become Orthodox. I think it is a tragedy that the Gallicans and other advocates of conciliar ecclesiology lost out to the ultramontanists, the latter of which eventually went on to give us Vaticans I and II, shattering the Roman Catholic world.
tl;dr: In light of the ecumenical councils, how can one reject the fact that conciliarity is the proper fashion in which matters of Christian doctrine should be decided? How can you expect a conciliarist, such as myself, to accept as dogma those things (all Roman Catholic dogmas after the 7th council) which were not debated and accepted in council?