Not all hunting is illegal. Hunting deer, rabbits isn't. But it should be. There are ways to get food already. There's little to no reason people hunt deer other than trophy hunting.
Though hunting purposes aren't necessarily mutually exclusive. I've hunted a whitetail, ate it, and made a comfy rug out of its hide. Had buckskin bracelets made for my fiancee and sisters.
Let's not be presumptuous with our reasoning for banning game.