I have a hard time with killing animals just because they are annoying. I understand why farmers kill gophers but I still dislike it (why can't they let the coyotes have the gophers?). I even tend to move bugs outside rather than kill them - except mosquitos, I admit. But oddly enough, I don't have any problems with hunting; I think the difference is in the intent.
Humans are animals, and carnivorous ones at that (actually omniverous, but that includes carnivorous meals). So it is in our make-up to eat meat, which means that someone has to kill it first; since we aren't generally scavengers, that means humans have to kill other animals to eat them, just as lions and wolves do. But we are also human, which means that we shouldn't kill mindlessly; we need to respect the animal that is giving its life so that we can eat it. This philosophy means that hunting an animal, with respect and in a fair chase, is morally acceptable to me; and yes, fair chase means what it says: we miss far, far more pheasants than we hit each fall. It also means that raising animals for meat is fine as long as the animals have some kind of natural life (cattle eat grass in open pastures, chickens scratch for grain, etc.) that respects their instincts, and are killed humanely. This is part of the natural cycle.
Respectfully eating animals that have been raised and killed humanely is much more morally acceptable than ignoring the whole issue, pretending that meat comes from some kind of plant before it is wrapped in plastic in the grocery store. This is why I want my kids to know where their meat comes from, whether that means helping brand cattle in the spring or hunting for pheasants in the fall. I want them to know that an animal has given its life for their dinner, so that they appreciate the animal and the food, rather than taking it for granted. If an animal is going to die, it should be honored at the meal. (For that matter, all food should be appreciated and honored, which is one reason we pickle vegetables and bake bread and make yogurt.)