The answer to 'shower won't flush' is that the most common causes are a clogged drain, a faulty shower valve, or a problem with the water supply. Symptoms may include the shower not draining properly, water backing up, or the shower head not producing enough water pressure. Solutions can range from using a plunger or drain snake to clear a clog, to replacing the shower valve or checking the water supply line.
If the issue is a simple clog, you may be able to fix it yourself with some basic plumbing tools. However, if the problem is more complex, like a faulty valve or a problem with the water supply, it's best to call a professional plumber to diagnose and repair the issue properly.