There are several possible explanations for a cat licking a person and then biting them:
1. Playing and practicing hunting skills: Cats may play by simulating hunting behavior. Licking you may be a gentle prelude, while the subsequent bite imitates the tearing action after hunting.
2. Over-excitement: During play or interaction, cats may sometimes become over-excited and unable to control their bite force, which may result in unintentional bites.

3. Communication methods: Cats may use biting to convey certain messages, such as telling you that they have played enough or that it is time to stop a certain activity.
4. Dental and gum care: Sometimes cats clean their teeth or gums by gently biting, and they may mistakenly use your fingers or other body parts as tools for cleaning their teeth.