The term is 'pescetarian', actually, and I am one

The rise of the non-veggie vegetarian

Why do I eat fish but not other animals? Because I have and can kill a fish myself. I can't bring myself to do the same for other animals, and I believe that if you're going to eat it, you should be willing to do so. People nowadays buy meat in pre-packaged cuts and really have no connexion to their food animals anymore. But that's also why I don't mind responsible hunting--so long as the meat is being used for food, and the animal is hunted judiciously. So I'm certainly not your average vegetarian, although I have described myself as a 'vegetarian who also eats fish' because it's just easier.