Let me explain how I see the matter, in relatively simple terms not because I’m talking down to anyone but to enhance clarity.
The bishops as a whole are the teachers of the Church as a whole. Ordinarily this teaching takes place at the local level, and this is good and normal. The danger does remain though that a bishop will depart from the truth, since Christ’s promise to preserve the Church applies to the Church as a whole, not to individual dioceses/eparchies with their individual bishops. Indeed, we know many bishops, and even whole groups of bishops, have fallen into heresy and schism over the years. This is why the Church was endowed with a visible point of unity that can itself (himself) interpret doctrine, in the form of a head bishop so to speak, with whom all must remain in communion if they are to remain in the Catholic Church, and who can clarify what is the true Catholic faith and what is a misrepresentation.
Because if this unique position, the bishop of Rome can essentially speak for the whole body of bishops put together, since he is this great reference point for all faithful Christians to recognize both the visible bounds and the authentic teaching of the Church of Christ. Likewise he can grant (or withhold) this same universal authority to meetings of bishops, whether by presiding over such a council and giving it that authority at the time, or through granting its documents that authority later by recognizing it as an ecumenical council. A council cannot be ecumenical without this recognition, even if every bishop other than the Pope participated and declared it ecumenical (which has never happened), because the rest of the bishops must be in union with the point-of-reference bishop for it to be an act of the Magisterium as a whole, rather than a lower level synod analogous to an individual diocesan bishop’s teachings.
[It’s true the bishops’ ordinary, diffuse teaching can be universal and therefore infallible as well, but only when all the bishops throughout the world, in union with the bishop of Rome and each other, agree and teach that a matter of faith or morals is to be definitively held. Thus when there is a contradiction between the teachings of two individual bishops then neither bishop’s ordinary magisterial teaching can be considered universal magisterial teaching. But by its very nature this Ordinary and Universal Magisterium doesn’t touch internally controversial matters, so the main thing we are talking about is the Extraordinary Magisterial teaching of Popes and Ecumenical Councils and Ordinary, not Universal teaching of individual bishops.]
It seems to me that if, when universal Magisterial authority is explicitly exercised to bind “all the faithful” to a doctrine or dogma, there is a group of Catholics that are inherently exempt from this due to some special status in the Church, then the Magisterium as a whole can no longer function. It merely becomes local groups of bishops teaching local groups of the faithful (however large a percentage of total Catholics one group may be).
Such an authority would not be infallible, since an attempt to bind all the faithful to an error would not bind the entire Church to error, but rather it would be like an individual bishop attempting to bind his local flock to an error. No matter how much power he may claim, he would never have it, since the faithful could still reject his teaching and remain faithful to the Magisterium as a whole. Only if the individual or group can speak for the whole Magisterium would it be possible for the Magisterium as a whole to teach error, and only this would constitute an utter failure of the Church (when it comes to issues of teaching, that is).
What you end up with in such a case is a Church much like the Orthodox Church, incapable of exercising universal teaching authority on any internally controversial subject, despite such authority apparently being recognized in the first eight centuries of the Church. Teachings on the Papacy in Vatican I and Vatican II would need to be rejected, not only by Eastern Catholics but by Western Catholics as well to remain faithful to the truth, since the whole idea of Papal infallibility rests on the ability of the Pope to bind the entire Church to a belief. Some kind of local binding power with local infallibility would not only not hold water since the whole logic of infallibility rests on Papal and Conciliar authority being universal, but to admit infallibility that applies to one person but not to another would relativize truth, defeating the whole idea of actual objective revealed truth. Meanwhile if we did admit local binding power
without local infallibility and
with an objective idea of truth it would mean bishops can force individuals into heresy and in fact have done so on the issue of infallibility. I think we can all agree that would be abominable.
Anyway, hopefully you can understand where I am coming from and why I consider perpetual universal extraordinary magisterial authority something to be insisted on, that I’m not just some pigheaded Latin who loves to bully those funny-looking Easterners.
Clearly there are other Eastern Catholics out there, including the Melkite bishop I quoted and mardukm, who do accept universal extraordinary magisterial authority while proudly retaining their Eastern identity.