I can think of three reasons why a domestic cat might bite their owner during petting. The first is often discussed which is that domestic cats can be overstimulated by petting whereby the cat interprets it as play and, as we know, play incorporates biting. It’s not malicious biting but what I would describe as play-biting. This can be quite firm to the point where it hurts a person but it doesn’t hurt another cat so much due to greater tolerance and protection by fur. Although, in play, cats can scream their objections when bitten which signals to the other cat that they’ve reached the limit of their tolerance to the play-biting.
The second reason is more subtle, which is that it is a signal that a domestic cat has reached the limit of their acceptance to being petted. It might be hard for some people to accept that their cat has a limited tolerance to being petted. Petting is enjoyable both for the person and the cat but cats don’t automatically like it. They like it to varying degrees depending upon the character of the cat. And all cats have a limit to what they will accept or enjoy. I think this mirrors the behaviour of people. Humans have a limit to being petted and touched. It is perfectly normal.
It doesn’t only happen between human and cat. In mutual grooming sessions between two cats (allogrooming) the interaction can be abruptly stopped sometimes when one cat suddenly turns towards the other and bites them. It won’t be a heavy, aggressive bite but it will be a clear signal to stop. It indicates irritation.
There may be preliminary signals to the final one, the bite, indicating that the cat has tired of being groomed such as tail twitching, restlessness, nibbling and I would add skin twitching or rippling. To me this always indicates a slight irritation in a cat and it needs to be observed and recognised by the owner. Some of these signals are quite subtle and if picked up by the cat’s owner they can help to understand when petting has gone far enough.
A third reason might be ill-health. If a cat has developed osteoarthritis and their joints are sore petting them in certain areas may be uncomfortable. This will cause limited acceptance and irritation. The cat’s reaction may be slightly distressing to the owner because it’s a rejection of their petting, an act of affection. Don’t take it that way. Cats are individuals and they should be respected just like people and their health requirements noted. Picking up cats can also be rejected by a cat because it is painful due to ill health.
P.S. Linda P Case suggests ‘counter-conditioning’ in which cats are fed tidbits during petting as a means to stop biting during these sessions.