No one else has mentioned this, but dissection is often cited as part of a carnivore's prey drive. This is most often discussed in dogs, e.g.
Predatory Behavior in Dogs, but is likely to be relevant to other predatory species likes cats.
It is possible that your cat's observable behavior is a form of play, which often contains components of the predatory sequence. It could also be boredom, a type of marking, a self-reinforcing tactile experience, a thwarted chewing/dissection instinct, or any number of other things.
The behavior may be prey-drive related. In particular, it may be related to the dissect step of the sequence. The predatory sequence steps vary by source, but are often defined as:
One web site references Dogs, A New Understanding of Canine Origin, Behavior, and Evolution by Raymond and Lorna Coppinger, University of Chicago Press, 2001; page 116 as the source of one variation of this sequence.
If this behavior bothers you, and once you've ruled out medical issues, you can try a number of things to see if they reduce or redirect the behavior.
- Offer more suitable objects with a similar taste or tactile feel, which may satisfy the oral component of the behavior.
- Switch to a raw diet that includes raw meaty bones, which may satisfy the chewing or dissection instinct.
- Treat the area with a pheromone like Feliway to see if scent-marking is a component of the behavior.
- Feed your cat through treat balls (e.g. Kong Active Treat Ball for Cats, feeding puzzles, or other boredom-fighting objects to see if this satisfies your cat's play or prey instincts.
- Keep lots of spare boxes on hand, as chewing boxes (as long as it doesn't result in a medical issue like intestinal blockage) seems like a relatively harmless pastime.
You can't ask your cat why he's chewing the boxes. Empirical evidence and the process of elimination are your friends in cases like this.