The answer to 'why is my air duct grimy' is that air ducts can become dirty and grimy over time due to a buildup of dust, dirt, and other airborne particles. This can happen as a result of poor indoor air quality, infrequent cleaning, or issues with the HVAC system. Symptoms of grimy air ducts include reduced airflow, increased dust and allergens in the home, and unpleasant odors.
The best solution is to have your air ducts professionally cleaned every 3-5 years, or more frequently if you have pets, smoke indoors, or live in a dusty environment. While you can attempt some light DIY cleaning of accessible areas, it's generally best to hire an experienced HVAC technician to thoroughly clean and inspect your entire ductwork system.