The answer to 'why is my heat exchanger smells bad' is that a malfunctioning heat exchanger can release unpleasant odors. This is often caused by cracks or leaks in the heat exchanger, which allow combustion gases to escape into the air being circulated through your home. Common symptoms include a sulfur or rotten egg smell, and the odor may worsen as the unit runs.
If your heat exchanger is producing a foul smell, it's important to have a professional HVAC technician inspect it as soon as possible. Attempting to repair or service the heat exchanger yourself can be dangerous, as it involves working with combustible gases. Only a licensed HVAC technician should diagnose and repair issues with your home's heat exchanger.