Why cats always lick their fur:
1. The most basic way cats groom themselves is to clean their bodies. Cats are clean animals and can be quite fastidious.
2. Cats lick their fur to relieve their tension and stress. 
3. If a cat has a skin disease or parasites, its skin will be very itchy, and the cat will be unable to resist licking and biting that area of skin frantically.
4. When the ambient temperature affects a cat, licking its fur may be a way for the cat to regulate its body temperature.
5. Cats licking their fur can also be a form of compulsion. There's nothing wrong with cats licking their fur normally, but if a cat has experienced something, it needs to keep licking its fur to stay calm.