One thing you can do is to make sure that your nipples are fully erect before your cat starts nursing. If your cat is nursing from you, there are a few things you can do to try to stop it from biting your nipples. Another possibility is that your cat is trying to groom you and is biting your nipples as part of its grooming routine. One possibility is that your cat is nursing from you and is mistakenly biting your nipple instead of the teat. There could be a number of reasons why your cat is biting your nipple. Seeking Professional Advice for Aggressive Nipple Biting.Training and Redirecting Nipple-Biting Behavior.