TDAXP once told me a story of how a textbook of his said that the "Far East" is called such because if one were to travel east from America that is where one would end up. The same book proclaimed Emperor Constantine I was the founder of the Holy Roman Empire.
The terms "West" and "East" are based on interpretations of the development of civilization. The West has its foundation in Ancient Greece while the East at first was Asia, meaning usually Persia. The West saw itself based on logic and limited government while the East believed in their god-kings supremacy. As time progressed Europe and European-based cultures inherited the term the West. The term "Far East" originated out of the desire to differentiate classical Asia from China and Japan, which Europeans were late in learning about.