A cat allergy, whether to something in the environment, something in the diet, or insects such as fleas, often plays out on the skin. A cat that has an allergic reaction can become chronically itchy to the point that all the licking, chewing, scratching, and biting at the uncomfortable spot(s) can cause her hair to come out. It can also cause something known as miliary dermatitis, a skin condition characterized by crusty lesions. (Miliary dermatitis is also known as scabby cat disease.) Often, an allergy causes the skin to become inflamed, too, among other reactions.