The answer to 'why is my central air smells bad' is that there are several common causes, including mold or mildew buildup, a dead animal in the ductwork, or a problem with the drain line. Symptoms can include a musty, moldy, or rotten odor coming from the vents.
If the smell is coming from the vents, it's likely due to mold or mildew growth in the ductwork or coils. This can happen if there's excess moisture in the system. You may be able to clean the coils or ductwork yourself, but it's best to have a professional HVAC technician inspect and clean the system to properly address the issue.