The Orthodox Religion split with Rome during a prolonged exit. Going back to the initial break, it concerned who was the successor of Peter.
The early Church proclaimed the Bishop of Rome as the legitimate successor of Peter. So, there were two claimants, along with a French bishop, who all claimed the right of the papacy. The French bishop gave up his claim, but the other two each claimed to be the true successor of Peter.
This was caused by the Roman Empire fracturing. In the end of the Roman Empire there were co-emperors, one based in Rome and one in Constantinople. They had staggered terms, and each reigned as a co-emperor. When the barbarians finally had the Western Roman Empire is disarray, the Eastern Roman Empire held back troops, keeping them for its own protection, thereby allowing a collapse of part of the Western Empire. Now came the question of what did the early Church consider the Bishop of Rome? One bishop was Bishop of the City of Rome, the other was Bishop of the remaining seat of the Roman Empire. So, which Rome determined the successor of Peter? Was it the city or the country?
In hindsight, there no longer is any Roman Empire. Yet the City of Rome remains.
Of course, it came down to more that who was Pope, there was a difference of opinion on a major religious idea that Jesus is both fully God and man fully. This would be difficult for an early century person to determine, except through the teachings of his or her bishop. Hence, people followed their bishop. I believe this issue is now resolved, and the Orthodox Church no longer holds Jesus to not be fully man. (I am not an authority on the Orthodox Church, so I may be in error here.)