Well we have to eat, and humans are omnivores, had our long lost ancestors not eaten meat then it is unlikely we would have developed as sophisticated brain as we have and would most likely still be living in the jungles of Africa. Taking that into account "humane" killing becomes a process of ensuring that as little suffering is felt as possible by the animal. Inhumane killing I believe is killing where the aim is purely for fun (hunting, with no intent to eat the kill) or treatment that is tantamount to torture, such as beating an animal, before finally killing it.

Humans are meat eaters so given that, it is difficult to propose an argument that "humane" would exclude eating meat. What being humane does mean is that the killing was compassionate and animals did not suffer.