Licking is a common behavior for cats, usually to keep their fur clean and smooth. Cats sometimes bite their fur, possibly because they are finding lice or other parasites while licking their fur and trying to get rid of them. It may also be that the cat is irritated when licking its fur, causing them to bite it.
If your cat often bites its fur, you may need to take it to a veterinarian to determine whether there is a health problem. resulted in this behavior. It could also be that your cat is feeling stressed or anxious, causing it to start chewing on its fur to relieve the stress. In this case, it may be helpful to take your cat to see a pet behaviorist or pet psychiatrist.