Papal authority can be interpreted either way.
As for why we reject Papal Supremacy, we reject it because it is a later innovation made by the West to give it an excuse to interfere with the East.
I have come to the conclusion that Rome was granted certain privilages that are generally denied by the Orthodox (such as the right to be final arbitrator in disputes), however given that several of the Seven Ecumenical Councils had Rome missing from crucial stages (if it was involved at all), then you have to question the whole argument that Rome is an integral part of what makes a council “ecumenical.”
Simply put we reject the idea of a Papal Monarchy because there is nothing to back it up.