I wouldn't want to shoot birds, rabbits, deer but that doesn't mean I feel outraged by photographs of people who do this. Pheasants are bred for the shoot on country estates. It's a business, some people pay to have a day's shooting, the retrievers get an outing and its seen as good revenue raising , productive business.
Deer hunting is something I find distressing but that's because I see them happily roaming on local moorland. In some areas their is a need to cull them. We no longer have wolves in Scotland, that would be an ecologically sound way to keep the population down I suppose, though no doubt the wolves would also eat cattle and sheep. It looks as though an organised shoot that raises money and manages the deer population is the way to go.
I have occasionally been vegetarian, don't eat a lot of meat and always try to buy from reputable sources.
I honestly can't see the difference except that animals in slaughter houses probably endure more terror than those killed by a single shot. Either we don't eat meat or fish, anything with a face frankly or I don't think we can criticise folks, even PrinceWilliam.