The answer to 'why is my drain trap won't flush' is that the drain trap may be clogged or obstructed, preventing water from flowing through properly. This can happen due to a buildup of debris, hair, soap scum, or other materials that get trapped in the P-shaped bend of the drain trap.
Some common signs that your drain trap is clogged include slow draining, gurgling noises, or a foul odor coming from the drain. In some cases, the clog may be deeper in the plumbing system, but the drain trap is often the first place to check.