I'm sorry, but, not to open a whole new can of worms, but "all animals not bred to be killed and eaten by man"?
So, you do not support hunting, but you are supporting the meat industry. I can guarantee you this, the animals that are hunted and shot will almost always live a better, healthier happier life and suffer a much more humane and quicker death than those in captivity that are bred for it [the meat and other elements are best if one can quickly obtain the animal, meaning a quick kill is favored by far, and practiced for by hunters - but the meat industry...eh, you can do some research of that on your own]. Just take a look at factory farming and the meat industry.
[Note I am the reverse of advocating hunting for "sport" and never, ever will you see me endorse such maladaptive, rash, and pointless behavior - no offense meant to those that may do so, but this is how I feel]
As it is, "predators" and "prey" alike can do damage property, damage to other natural elements (deforestation due overpopulation, lowering of vital prey populations due the same, etc.), and they often do (thanks to human meddling with the order they once held to begin with) have to be kept in check population wise. Sad by-product of civilization. Whether it be trying to increase, maintain, or lessen the size of the population - depending on situation.