Why aren't we eating Asian Carp?

The simple answer is lack of demand.  It is considered by Americans to be an undesirable fish.  Ever see certain types of fish going for $15, $20 or $30 per pound? The Asian Carp wholesales for $0.15 per pound.  This article provides some interesting insights on the subject. http://www.stltoday.com/business/local/article_9492759b-5968-5021-9c13-23168664f0d3.html

To expand a bit on Garrick and John's answers: 1.) Carp are bottom-feeding fish, which makes them much more likely to pick up toxins, chemicals, and generally unpleasant flavors from the wild. (Surprisingly enough, their mercury levels are low since they generally don't eat other fish.) Carp is often described as having a "muddy" flavor for this reason, and if you ever wondered why carp is often served with hellishly spicy sauce in Chinese restaurants, this might be why. A parallel can be made with the North American catfish, which, due to its bottom-feeding habits, is one of the few fish in existence that is better when farm-raised rather than caught wild. 2.) Carp's bone structure makes it extremely inconvenient to fillet and eat. Most Americans with the luxury of better-tasting and more easily-available fish aren't going to relish the thought of playing "find-the-pinbone" every night for dinner. There have been a few chefs (I think Anthony Bourdain mentioned it in one of his books once) proposing that carp and other kinds of normally unpalatable fish be ground up and turned into fish meatballs, similar to Japanese surimi. Assuming anyone ever works out the production costs and labor intensity involved with processing carp, this could actually turn out to be a good idea for combating both hunger and carp invasion. Also, Asian carp shows up on the menus of certain "invasivore" chefs hoping to spread awareness about the issue. For the most part, though, we don't eat carp because there are better choices.