The answer to 'why is my P-trap won't flush' is that a clogged or obstructed P-trap is the most common cause. The P-trap is the curved section of pipe under your sink that is designed to hold a small amount of water, creating a seal that prevents sewer gases from entering your home. If this trap becomes clogged with debris, hair, or other blockages, it can prevent proper flushing and drainage.
Some common symptoms of a clogged P-trap include slow draining sinks, gurgling sounds, and foul odors coming from the drain. To fix this issue, you'll need to first try plunging the drain or using a drain snake or auger to clear the blockage. If those DIY methods don't work, you may need to disassemble the P-trap and clean it out manually. If the problem persists or you're not comfortable doing the work yourself, it's best to call a professional plumber to diagnose and resolve the issue.