As a Brazilian (see previous comments about the Wright Brothers), I consider that an airplane:
* Is powered, otherwise, it's a glider;
* Can maintain level flight, otherwise, it's just "Falling with style";
* Can take off on it's own, assistance (RATO, catapults) is allowed for short take-offs (like from a carrier);
The Shuttle fails in all that in some point of the flight or another, Buran on the other hand, could be fitted with air breathing jet engines that allowed it to do all that.
I like Douglas Adams' description: The ship hung in the sky in much the same way that bricks don't.
Well, by that definition I think the X-15 isn't a plane - it required a B-52 mothership to launch after all. IMO it's hard to find a definition of "plane" that includes the X-15 but not the Space Shuttle stack (not the orbiter on its own - the full stack).
And on descent it was gliding, not under its own power.