The answer to 'why is my water softener won't flush' is that there are several common causes, including a clogged drain line, a problem with the control valve, or issues with the brine tank. Symptoms may include the water softener not going through the regeneration cycle properly or water not draining from the system.
Some solutions to try include checking the drain line for clogs, cleaning the control valve, and ensuring the brine tank is filled with salt. If these DIY troubleshooting steps don't resolve the issue, it's best to call a professional plumber who can diagnose and fix the problem.