I don't see anyone asking the obvious question.
Turkey joins a world war in which it has to fight either the biggest bully in town (Germany) or the oldest and most feared bully in their neighborhood (USSR), or possibly both (remember they're friends in 1940) - in order to help the Greeks?
Yabbut... Though it seems incredible, approaching ASB, the OP has a scholarly cite that Turkey actually threatened to do this. (Or at least to fight Bulgaria, and by extension Italy; Germany only came into it later, and there's no reason to think the USSR would Do Something.)
So that obvious question was answered already.