The answer to 'drain won't flush' is that a clogged drain is the most common cause. This can happen due to buildup of hair, soap scum, food particles, or other debris in the drain pipe. Symptoms include slow draining, gurgling sounds, or a completely blocked drain that won't flush at all.
To address a clogged drain, you can first try using a plunger to dislodge the blockage. If that doesn't work, you may need to use a drain snake or auger to physically remove the clog. More severe clogs may require removing the drain pipe and clearing it out manually. If you're not comfortable doing this yourself, it's best to call a professional plumber to diagnose and fix the issue.