First, with respect to eating them. No it's not necessary to live, but there are reasons:
1. I agree that harvesting an animal from the wild is in a sense morally superior (IMO) to eating meat from animals raised in farms, in little cages, in terrible conditions, genetically engineered to the point where they can't walk from having such meaty bodies, etc. At least the critters I harvest had their lives up to that point to live free, and naturally. And they have a pretty decent chance of living their entire lives without being shot. No so for captive-raised meat consumed by the public. You could make a pretty decent argument that eating commercial meat is immoral, whereas hunting is not.
2. In addition, the meat I eat from wild animals is not contaminated with tons o' antibiotics and such that are injected into commerically raised animals. Plus, they're much leaner. As a result, it's arguable healthier. Perhaps not as healthy as a vegetarian diet, but healthier than commercial meat, IMO.
3. There's a certain definite satisfaction from eating game that you've harvested with your own hand. Very mentally satisfying. This must be a primal urge, dating back to cavemen days. Stronger in men than women, but present in some women too.
4. If you're really good, and hunt enough, you can actually save money over store-bought meat prices in the long run, once you've reached the break-even point and covered the initial outlay cost of your gear (guns, hunting equip, etc.). Granted, the venison I've eaten is well over $100/pound, when you factor this stuff in, but over my lifetime, that unit cost will come down, down, down, and eventually be a plus instead of a minus financially (or so I would like to think - provided I don't pay for a bunch of fancy guided hunts in AK, Can, Africa, etc. - then my meat would be very expensive indeed)
Next, to control pests/varmints:
-Many species are devastating irritants to our livestock, crops, infrastructure, pets, etc., and need to be culled to varying degrees, and some to the largest extent possible without making them become endangered, in many people's opinions anyway, including coyotes, crows, beavers, feral pigs, nutria, mice & rats, prairie dogs, moles, and other rodentia. Perhaps arguably skunks, though I don't view skunks as a problem. I suppose they can carry rabies, but so can dogs for that matter. Deer are also a nuisance in a sense, as mentioned, due to the ticks they carry and spread, and the cause of motor vehicle accidents.
