The answer to 'why is my shower won't flush' is that the shower drain is likely clogged. A clogged shower drain can prevent water from draining properly, causing the shower to not flush or drain slowly. This is a common plumbing issue that can be caused by a buildup of hair, soap scum, and other debris in the drain pipe.
Some common symptoms of a clogged shower drain include slow draining water, standing water in the shower, and foul odors coming from the drain. To fix a clogged shower drain, you can try using a plunger or a drain snake to clear the blockage. If these DIY methods don't work, you may need to call a professional plumber to inspect the drain and use specialized tools to fully clear the clog.