Rome did not separate from the One, Holy, Catholic, Apostolic and FIRST Church founded by Christ on the apostles, the first Bishops.
Where are you getting your strange ideas?
... the Church split along doctrinal, theological, linguistic, political, and geographical lines, and the fundamental breach has never been healed, with each side sometimes accusing the other of having fallen into heresy and of having initiated the division.
Or is this not in your history book?