But, the Pope is more than just first in honor. The Bishop of Rome was from the earliest days (I won't say from the the beginning) the pre-eminent bishop in the Church, the presiding bishop, the "elder" bishop, but not a "supreme priest" (pontifex maximus), a pagan title +Leo arrogated to himself; nor was he the ruler of the Church although the papal legates liked to use that term.
The Orthodox, of course, recognize the Pope's right to primacy in honor, but reject the biblical interpretation of his supremacy, his title as the Vicar of Christ (also arrogated by a pope in the 5th century based on one of Syrian Father's opinion in the 4th century), "Prince of the Apostles," etc. as human innovations and titles and powers never bestowed by an Ecumenical Council.
Petrine supremacy is equating uninspired bishops of the city of Old Rome to the inspired Apostle, by virtue of his office alone. No other patriarch does that, although they all can trace their roots to one of the Apostles. Thus, when the bishop of Constantinople speaks, no one says "John spoke." No Eastern bishop lives under the illusion that his office entails the same qualities his apostolic predecessor possessed. But when the Pope speaks, they say "Peter spoke." Rubbish! It amounts to a personality cult.
His supreme authority as a bishop above all bishops is clearly stated in Roman Catholic Catechism: "the Roman Pontiff, by reason of his office as Vicar of Christ, and as pastor of the entire Church has full, supreme, and universal power over the whole Church, a power which he can always exercise unhindered" [paragraph 882], and "The Pope enjoys, by divine institution, 'supreme, full, immediate, and universal power in the care of souls'" [paragraph 937].
I can assure you that this is not the understanding the Church had in the first millennium. It is almost impossible for this to be rescinded, even if ignored, removed, reworded, etc. without in some way admitting it is wrong. And without such recension no unity will ever be possible.