When you completely cover one eye, why does the brain seem to shut it off? why do you only see out of the other eye instead of a mix of both eyes as you would with something in front of one eye?

It is whats called eye rivalry. If when you cover on eye and the vision from the covered eye were to enter the other eye it will become transparent. So the brain decides to just shut that part off so the suppression may be balanced. (Like two different orientations of a stripped pattern in opposite eyes)