These ideas aren't simple at all. They're profound. They certainly don't occur to animals. Yet evolutionists claim that our ancestors were animals. If that's so, then this allegedly basic morality must have evolved. If so, let's hear how. If evolution is correct, it shouldn't be that hard to postulate a reasonable account.
But there is none, because evolutionary pressures would always favor the guy who promoted reality in public but privately took whichever woman he fancied. (e.g. "Religion [and its morality] is the opiate of the masses.") If morality had evolved, humans should accept this hypocracy as ethical, but the vast majority of us is repulsed by it.
I just did. And, by the way, 'thou shalt not kill' and 'thou shalt not steal' have been so often ignored in the last century, I think it's a real stretch to claim they're any kind of innate human trait. People most certainly kill, often and for very trivial reasons. They steal like bandits. We can certainly propose mechanisms by which humans might have evolved an innate moral sense. Whether they in fact did evolve one is very much an open question.
Never had dogs, I take it. Dogs have an extensive moral code. They obviously can't verbalize it, but they live it.
Ever watch dogs play? They have an uncanny ability to bite at each other without closing their jaws. It's really amazing to watch.
Moral codes do not need to be written down or reduced to rational arguments. They can be embodied. And animals are not all self centered. There are many species where individuals restrain their self interest in favor of the group. In fact, this is a universal trait in mammals.