It is an odd category, and Japan is often considered to be "Western" - these days at least. That certainly wasn't the case even a few generations ago.
I think it's ostensibly supposed to be more about shared cultural values, but even that is a pretty weak way to divide countries. Perhaps "an ally of the United States" is a little more accurate?
Any societal dividing line like this is bound to hit on problems once subjected to the real world.