Reasons why cats lick their fur:
1. When cats feel anxious or uneasy, they will also lick their fur to relieve their emotions and release stress.
2. When a cat is infected with parasites, causing skin discomfort, it will lick the affected area incessantly. The owner should take it to a veterinary hospital for treatment as soon as possible. 
3. If cats get along well with each other or have quarreled, they will lick each other's fur to express affection and repair their relationship.
4. If a cat is deficient in vitamins, it will supplement them by licking its fur. The owner should feed the cat pet trace element tablets.
5. Cats are very clean animals and often lick their fur to keep themselves clean.