Why is carburetor heat use discouraged on the ground?
If you feel that you would need carb heat sitting on the ground, I'd recommend taxing back and waiting for conditions to improve. If you are set on going, usually doing a run-up at the runway before take-off will tell you if you have carb ice or not.

The other answer gave good reasons, sucking in some FOD (foreign object debris), but there are some other things you would want to consider...

Forgetting to push the carb heat back in before takeoff
 - Especially important when taking off from short fields, you want all the power your engine has to offer, as carb heat robs your engine of some power. If you have carb ice, applying carb heat will cause your engine to make even less power (hot air is less dense than cold air). 3/4 of the way down a 1200 foot runway is a bad time to realize the carb heat is still on, because it probably isn't on your takeoff checklist.

Carb heat is not very effective on a cold engine
 - This is a real problem when you are at idle or especially gliding, the airflow over the engine components and the exhaust just doesn't create enough heat to melt the ice in the carb (at least not very quickly). This is why you may be instructed to "clear" the engine periodically during low power operations. This involves adding power and then carb heat to help melt any ice.

That all being said, its not so much a rule as a recommendation. You'll probably find that during your flight training you'll end up leaving the carb heat on while on the ground for short periods. This happens a lot during landing operations when you are instructed to have carb heat on (my instructor taught me mid-field downwind, "Seat Belts, Gear, Fuel Selector, Carb Heat, Mixture, Prop, Power"). You'll end up leaving it on until you've cleared the runway (or set up for a touch-and-go) and are running your "after landing" checklists.