This article is from the Problem Behaviors in Cats FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Some cats may develop the annoying and expensive habit of ripping up carpet. There are several possible reasons behind this, listed below. In all circumstances, be sure that there is plenty of items that the cat can scratch.
* Other "approved" scratching posts may be made of carpet, confusing your cat. Switch to scratching materials that do NOT use carpet. Common alternatives include sisal rope, corrugated cardboard, or carpet turned wrong-way out. Retrain your cat onto these items.
* Some cats rip at doorways that are closed, trying to get through. You can put down plastic carpet covering, securing it with nails if necessary, through the doorway so that it sticks out on both sides.
* A particular spot may be favored, for no apparent reason. There may be some odor at that spot. Try cleaning it thoroughly with an enzyme-based cleaner like Nature's Miracle and then spraying a touch of Bitter Apple or the equivalent on the spot.