Eat what you kill is bull####. Gophers need to be shot. Crows need to be shot. Coyotes need to be shot. Feral cats in Australia and New Zealand need to be shot. Mice in your basement need to be trapped. Sure, you could eat them, but you certainly don't have to and anyone that tells you that it's unethical to shoot something and not eat is is an idiot that thinks they're better than you.
Want to shoot a deer and not eat the meat? You can donate it. Like I said to my brother a while back, if you can't give away elk meat to your friends, then you need better friends.
I would rather people said "kill what you eat". At least that serves to tie people to their food supply and doesn't allow them to divorce themselves from the process.