Contrary to popular belief, cats (and other animals) don't just bite to inflict pain or through aggression, but may also bite to be playful or even show affection. In other cases, a cat may bite to warn or remind someone that it has had enough of being played with at that time. In these cases, a cat will often not bite with enough strength to hurt, in which case there is nothing to worry about.
If your cat is biting aggressively, it is probably for a specific reason. Cats love attention, but there comes a point when all cats have had enough and want a break. If your cat becomes upset that you aren't leaving it alone, then it may bite. Cats also don't like to jumped on or approached quickly, and if they are may lash out in a natural reaction to a threat.
In general, cats are not aggressive animals with their owners. If your cat is biting aggressively, then that is a sign there is something wrong or amiss, and it is likely to be to do with the way you are treating the cat. Treat your cat with respect, and be observant as to how it reacts to different ways you interact with it. It should be possible to tell when a cat is upset, so you know then to back off and give it some space. Watch the cat for signals that it has had enough of being stroked for example, then you will know in the future when to stop.
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Richard Cross is owner of the Pets Clinic website [http://www.petsclinic.org]. Pets clinic provides information and advice about pet cats and many other pets, with new articles added daily.