Cats aren’t people. They don’t think like people. They’re a whole different ball of twine. So when people ask me why their cat bites, my answer is simple. Don’t think about it. Just fix it.
Since we don’t speak the same language as felines, we have to use our great big brains to guess how to fix the situation. Maybe using toys to play with the cat instead of using our hands will end the biting. Maybe the cat is bored and needs a half hour a day of play time with the owner. Maybe the cat has a sore spot and needs to see the vet. There are all sorts of fixes to try out.
If we try to psychoanalyze kitty, we’re going to wind up needing therapy ourselves. How do I keep myself bite-free when I groom cats? I try to be very gentle. I groom in quiet homes, instead of noisy salons. And I wear protective gear, because if kitty wants to bite, she’s going to bite.