Rome wrote the Code of Canon Law, and many Eastern Catholic hierarchs aren't the bit pleased with it.
First of all, no pre-1054 Eastern Christian recognized that the pope had the right to intervene in the internal affairs of the Eastern churches unilaterally. Pope Nicholas' uncanonical, unilateral, intervention in the case of St. Photios is a prime example because there was no appeal, and Fr. Dvornik has proven this was the case.
The patriarchs and their Holy Synods should have the right to elect and appoint their own bishops without papal approval based upon custom. No pre-schism pope appointed any Eastern patriarchs or bishops.
The papal claims to direct jurisdiction in the East were never recognized in the East.
False. For instance, see Pope St. Boniface I's letter "Manet beatum" of 422 AD to the Bishops of Macedonia. This decision appointing a new bishop for Corinth (with the claim being based on universal jurisdiction through Mt. 16:18-19) was recognized and submitted to. Likewise, Pope St. Agapetus I (535-6) deposed Anthimus, the Patriarch of Constantinople, against the will of the Emperor. This decision was recognized as correct by a later synod in Constantinople under Patriarch Mennas.