This is actually not good behaviour – what you have described. There is a difference between play and rough play. It’s a dominance thing with cats.
We don’t usually allow our cats to do this. It is most common when we are petting them. The cat bites down on the hand and holds the bite – sometimes grabbing the hand with it’s claws as well. Most people think it’s about love and they let their cats do this. When ours do, we say “No” sharply and stop petting (ignoring them). After doing this for about a month, they never bite me (they bite my partner as she doesn’t stick the plan as much).
In most cases, it is how the cat gains dominance and gets something it wants from you.
A quick way to help you figure out what type of biting behaviour your cat is displaying is to note when this happens. Were you simply petting them? Touching them in a specific spot? Is your cat young?
The dominance thing is usually whilst petting. Some cats, like humans, can be moody. If you are petting your cat and its tail starts flicking/body tenses, then you should stop – your cat is telling you it’s had enough petting. If it’s only when you touch a specific spot on them, they probably have an injury. If the cat is still young, it is learning how to behave (testing limits and its own strength) and you must teach it that your hand is not a toy. A person must learn their pet’s personality and quirks to get along with them in the end.
Each of our cats are different. One cat is super snobby and doesn’t like much petting at all. If you touch him, he will begin to clean himself frantically. One other cat can’t get enough petting and loves when you pull his tail or pat him hard but won’t cuddle at all. Another only likes to be pet on the head. The last one (my partner’s baby who’s incredibly spoiled) loves to cuddle and get in your face. Every single one of them has done the bite thing. The spoiled one stopped a long time ago. The other three still do it on occasion (to my partner).
There are different ways to teach a cat to stop this behaviour. You can find many of them online – if that is what you desire.
I hope some of this helps.