You would need to make further distinctions. If food is a valid reason for killing animals, is it also a valid reason for killing humans? Further, your argument has made the professions of cattle farming and butchery a crime, as neither kill animals for food but rather for profit. If this is the case, then I have serious issues with your three laws already. In any case, it doesn't matter - the reason those three (or two) laws aren't enough are because it leaves almost every instance of crime ambiguous or a matter of interpretation, and everybody will interpret them differently. Your clarification of any specific instance of crime is really just making more laws.
@Holk
I would argue that delusion and intelligence are interrelated - it is impossible to be deluded without intelligence. Delusion is an instance of intelligence. And, I cannot prove it, but in my experience delusion is a necessary product
of intelligence. Everyone who is intelligent entertains some delusion, myself included.
As for basic instinct - yeah, most people would not survive for that reason. But the world is overpopulated anyway lol. Seriously though, I don't regard the extinction of the human race as something particularly bad and it is certainly inevitable no matter what we do, unless we develop the means of space travel and send all humans to different galaxies, and that's excessive. Anyway, I think I would probably prefer the eventual extinction of the human race then the human race being permanently (until the sun no longer provides enough heat) stuck in log huts. :/