The answer to 'shower won't flush' is that a blocked or clogged drain is the most common cause. This can happen due to hair, soap scum, or other debris building up over time and obstructing the flow of water. Symptoms include slow draining, gurgling noises, and water backing up in the shower.
For minor clogs, you may be able to clear the drain yourself using a plunger or drain snake. However, if the clog is severe or the issue persists, it's best to call a professional plumber. They have the right tools and expertise to safely and effectively clear the blockage and ensure your shower drainage is working properly again.