The cat saliva which contains an allergen that causes allergic reaction in humans. Once a cat grooms herself, saliva is deposited on her fur which dries into dust and turns into dander or dandruff. These particles then are released into the air when a cat only moves about and especially when she is grooming or scratching herself. Brushing your cat doesn’t really help it either.
Word is getting loud that some research labs are attempting to produce cats that are free of the dandruff that causes allergies in people. They will try to use RNA interference to eliminate that particular gene in cats that produces the irritant, which is excreted through saliva and the skin.
So far, all cats produce the protein that will cause the allergic reactions in humans, even the hairless cat breeds.