"Why do we have a Middle East & not a Middle West? I say it because the Eurocentric worldview is the default way of looking at the world."
Actually, it's NOT Eurocentric. Europe is the West. No one in Europe (or America) calls itself the Middle Civilization. We're Western Civilization. The Holy Land and the Birthplace of Jesus was considered the center. Having to constantly go east to get there, though, sort of eroded that conception after a few centuries, though, and now the European worldview doesn't really have a Middle.
As for why there's no middle west, I would guess it's because while you're going east, it's civilization, civilization, civilization, but going west from Europe, it's just fishes. They could have subdivided Europe into the Middle West and Far West and such, but since the distinction tends to be at least partly related to progenitors, i.e., Middle East are descended from the Arabic civilizations, East from Indian, Far East from Chinese, &c., Europe just sort of generally considers itself the kid of the Roman Empire, which covered all Europe along the East-West axis, and even those countries that were left out tend to consider themselves its descendants, e.g. The Holy Roman Empire, and Moscow being the Third Rome.