The answer to 'why is my drain trap won't flush' is that a clogged or blocked drain trap is the most common cause. The drain trap is the curved pipe under your sink or bathtub that is designed to hold a small amount of water to prevent sewer gases from entering your home. If this trap becomes clogged with hair, soap scum, or other debris, it can prevent water from draining properly.
Other potential causes include a blockage further down the drain line, a problem with the vent pipe, or an issue with the drain opening itself. If the drain trap is not the problem, you may need to use a plunger, drain snake, or other tools to clear the clog further down the line.