Non-human animals don’t have immortal souls. If it is morally wrong–if it is “murder”–to kill an animal, then this has other repercussions as well. If we cannot kill them then we cannot eat them of course. We also cannot own them or sell them or even give them away (this would be akin to slavery). We cannot buy/sell or consume their products (eggs, milk, etc.), we cannot cage them in zoos, so on and so forth. Human civilization and its relationship to animals is based on the fundamental principle that the human being and the animal are two entirely different things, not merely two dissimilar things. I believe that we must yet have a good deal of respect for animals but more based on Who created them and gave them to us as opposed to anything an animal possesses that deserves such respect. Killing for the pure fun of killing I object to, but killing for sport AND harvest, I am wholeheartedly in favor of, especially since wild game is quite tasty.
Plus Jesus, as a devout Jew, had to eat lamb at least once a year at Passover, and He ate fish (at the feeding of thousands it can be safely assumed that He ate as well, and then there is the beautiful story of His post-resurrection breakfast of fish with Peter on the seashore). If Jesus is cozy eating animals, then I’m cozy with it as well!