Yep. I have a cat who only bites when he's angry, and another one who only bites when she's happy. Between the two of them, my arms look like I'm a heroin addict.
Breed the two to get to aggression neutral?
Breed the two of them to bite you whenever you move.
Or they just bite all the time.
Yeah... I guess I didn't think through all the edge cases on that.