The answer to 'why is my bathtub won't flush' is that there is likely a clog or blockage in the drain pipe. This can be caused by hair, soap scum, or other debris buildup over time, preventing water from draining properly. Common symptoms include the tub not draining fully or slowly, or water backing up when the tub is used.
Before calling a professional plumber, you can try some DIY solutions to clear the clog. First, use a plunger to try and dislodge the blockage. If that doesn't work, you can try using a drain snake or auger to physically break up the clog. If those methods are unsuccessful, it may be necessary to disassemble the drain pipe to fully clear the obstruction, which is best left to a professional plumber.