I couldn't bring myself to kill a living thing, unless its a bug or rabid dog. But a zombie Apocalypse would be awesome 
Make sure you stay out of the military then... lots of killing of living things going on. Even in training, such as survival school, you may be called upon to kill a defenseless little bunny. And eat it. And then go looking for more things to kill and eat.
Qualms about killing things just because they're living... Well, that's the business, taking living things and making them not-living. Even the refrigeration repair specialists and commissary troops have a role to play in the destruction of life in the military. There are plenty of good reasons to kill something or someone, so if that has a special horror for you that would render you incapable of killing when required to do so, then make sure you find another job.