What? Would you not prefer to reduce the pain in this world, whether it be animals or humans?

Would you not prefer to die quickly? While you may not agree with the rationalizing of killing the animal, killing it fast does reduce the amount of pain that it feels.

Humans are egoistic, yes, everything we do in the end we do because we benefit from it in some way, but that does not make good actions any less good, because whether or not they are made because you want to feel better yourself, they do improve the world, killing animals in a humane way > killing them in a non-humane way.