A cat might bite someone after sniffing them for several reasons:
1. Over-excitement: While playing or sniffing, a cat may accidentally bite you due to over-excitement.
2. Hunting instinct: A cat's hunting instinct may be triggered during the sniffing process, especially when they smell the scent of other animals or mimic hunting behavior.

3. Communication method: Biting may be one of the ways cats communicate. It may be trying to tell you that it is tired of playing or wants to stop the current activity.
4. Dental care: Sometimes cats will unconsciously use their teeth to clean their whiskers or face while sniffing. If your hand is nearby, it may accidentally bite it.