The answer to 'bathtub won't flush' is that the most common causes are a clogged drain, a problem with the bathtub stopper, or issues with the plumbing vent system. Symptoms may include the bathtub not draining properly, water backing up, or the tub not filling up when the faucet is turned on.
To troubleshoot, first try using a plunger or a drain snake to clear any clogs in the drain. If that doesn't work, check the bathtub stopper and clean or replace it if necessary. If the problem persists, there may be an issue with the plumbing vent system that will require a professional plumber to diagnose and fix.