For me, the issue is one of dominion. As I believe is true in most cases, if you prayerfully search the Bible for answers you are very likely to find them. The Bible provides many examples of Godly and righteous men using beasts for labor and food. In Genesis 9:3, God instructs Noah and his sons, "Everything that lives and moves about will be food for you. Just as I gave you the green plants, I now give you everything."
God wants us to use every resource of the earth to glorify Him. We were given trees and stones to build our shelters. We were given fish, birds, and animals for food. We were given fertile soil, water, sunshine, and seeds to cultivate crops. And God gave us the intelligence and physical ability to have dominion over all of these resources. To exercise our power and stewardship over these gifts in a respectful and conscientious manner is to fulfill God's desire for us to have a rich and satisfying life while on earth. I believe we sin if we abuse our relationship with nature by polluting or wasting what we have been given.
At the same time, I respect a person's decision to not hunt or fish... either for sport or to feed himself. In our modern society, we rely on many "experts" for our daily needs. We call on carpenters, plumbers, electricians, mechanics, doctors, dentists, etc. to provide the essentials as well as the comforts of life. For some, this dependency is a matter of convenience... for others it's a matter of necessity. Relying on someone else for food is really no different. This level of dependency is why so few would survive in a widespread, cataclysmic event.