The answer to 'why is my sink won't flush' is that the sink drain is likely clogged. A clogged drain can prevent water from draining properly, causing the sink to not flush fully. Common causes of a clogged sink drain include hair, soap scum, food particles, and other debris buildup over time.
You may notice signs of a clogged drain like slow draining water, gurgling sounds, or a foul odor coming from the sink. To fix a clogged sink, you can try using a plunger or drain snake to dislodge the blockage. However, if the clog is severe or you're unable to clear it, it's best to call a professional plumber who can properly diagnose and resolve the issue.