The answer to 'why is my garbage disposal won't flush' is that a clogged or blocked disposal is the most common cause. This can happen when food, debris, or foreign objects get stuck in the disposal, preventing water from draining properly. Symptoms may include a slow draining sink, gurgling noises, or a completely blocked drain.
Some potential solutions include using a disposal wrench to manually spin and clear the disposal, using a plunger to try to dislodge the clog, or using a disposal cleaning product to break down the blockage. If these DIY methods don't work, it's best to call a professional plumber to inspect and repair the disposal unit.