Cats bite their owners to demonstrate affection, colloquially known as a love bite, but also to warn that they are becoming over-stimulated and want to be left alone. Some cats are also more physically sensitive than others, becoming agitated from too much petting.
Soft bites that feel like a gentle press of the teeth against flesh are more likely to be signs of affection or a request to be left alone. However, some over-stimulated cats can become stressed and bite hard enough to break skin.
Kittens and young cats tend to play rough with each other, engaging in displays of mock aggression. While cats differentiate between solitary and feline play, some cats mistakenly romp with humans as they would another cat, causing injury. To train cats not to claw or bite hands and feet, end play sessions as soon as they become rougher. Redirect their attention to strings, balls or other toys, avoiding contact between their claws and human limbs. Never encourage this kind of behavior; while this type of mock aggression seems harmless and cute in kittens, they retain this behavior as adults and can cause serious injury. Do not physically punish them or try to block their access, as this can translate into play behavior and intensify their actions or trigger real aggression.