If you look at history, it makes sense.
The Church Christ founded was one for 1000 years, with bishops in Constantinople [added after the move to Byzantium], Alexandria, Antioch, Jerusalem, and Rome -- the bishop of Rome called "first among equals", which did *not* mean he was *in charge*.
The trouble started when the emperor Constantine moved the capital of the empire from Rome to the city he renamed Constantinople (now Ankara), lowering the prestige of Rome. Various divisive issues -- dogmatic, philosophical, political, cultural, etc. and including misunderstandings and at time deliberate mistranslations -- led to the Great Schism of 1054. Whereas up till then it was the Christian Church, new names were needed. The bishop of Rome became the first Catholic Christian pope, and the four remaining Christian bishops continued as authorities in the Eastern Orthodox Christian Church.
For centuries, people lived and died within a very small radius and not many were educated. In Western Europe it made no sense to talk about the Christian Church of the East so, as far as Catholics knew, THEIR Church was the first/only Church.
Both Churches have the Fullness of Truth, apostolic succession, and all the Sacraments.