I found an interesting comment on Unity Answers about why Unity uses left hand coordinates:
Unity was made by Western people. The convention for such people is that right is the positive direction. Put that together with what I said above; when you think left-to-right, then X being positive from the vantage point of the game object (which is often a character or camera), is the way to go.
No idea if this is indeed the reason, but it’s easy to memorize. Looking at Unity XYZ gizmo, if Z means to go forward, then turning to the right (the “right” or “positive” direction) means to turn where X is positive.