The answer to 'garbage disposal won't flush' is that a clogged or jammed garbage disposal is the most common cause. This can happen due to food debris, hard objects, or improper use of the disposal. Symptoms include water backing up in the sink or the disposal making a humming or grinding noise without flushing.
To troubleshoot, first try turning off the power and using tongs or pliers to remove any visible blockages. You can also try using a disposal wrench to manually rotate the blades and dislodge the jam. If that doesn't work, you may need to disassemble the disposal or call a professional plumber.