I CAN explain why we don't find them anywhere else in nature.The origin of morals in my view is our sentience.
Not religion.
I think that as a whole we realized that actions which cause the least suffering were best, i.e. moral. It's not that hard to imagine each and every moral's human justification absent religion. I can do each and every moral that way, one by one.
This is where I believe there is a flaw in your view. There are other sentient creatures in nature. Their morality is centered on animalistic instinct and what's best for the tribe. Yes, you can do all the rationalization, imagining and justification for how you think humans derived particular moralistic views not found anywhere else in nature, but you can't explain why we don't find these anywhere else in nature.
The human construct of morality is very much tied to our intrinsic awareness of a power greater than self. It is through this we became inspired creatures with the ability to conceive civilization. It also inspired us to create Religion.
Okay, harken ourselves back to caveman days, and you come to me with this idea that we should all get along and not kill each other because that's the least amount of suffering and is best for us... If I am the stronger dominate male cave man, you know what I am going to do with your idea? I am going to kill you and use your skull for a crapper. Why? Nature.
Because other creatures in nature are not as smart as humans are.
Same with cavemen. Humans were not at that point of intelligent reasoning yet. Pretty easy to explain.
That's it! very simple.