This appears to be a classic frustrated animal. Is the cat home alot alone (including when everyone is sleeping). Dogs tied up and neglected chew things, cats left during vacations repeatedly, chew things. Dogs who don't get enough exersize, chew things. Look at the personality of the cat. If it is a playful, fun cat, it may need another cat as a playmate/friend (although this is tricky with cats). It is looking for stimulation in its life. Animals don't have to many options to complain when they are unhappy. They sometimes engage in self destructive behavior, sometimes they destroy other things. Once a bad habit is established, it can be hard to break, but you need to start with finding out why the cat is unhappy and correcting this situation. Then if correcting the situation doesn't break the habit, that is step two. Good luck!