There are several meanings to this story. It describe how evil came into the world by people blaming their problems on others and then trying to kill them - scapegoating, the way Adam blames his transgression on Eve and Eve blames it on the serpent, which is a symbol of envy and hate.
Obviously, "evil" involves hate and envy and blaming your problems on others (politically, this is what leftism is).
Yet, there is more to the story.
I've always considered Adam and Eve to be about three years old. They're not self-conscious. Then after eating the fruit, they become self-conscious and realize they're naked. They also know "good and evil."
Animals, which are not self-conscious, can't be evil. They eat each other, but don't torture and maim. People do, and get pleasure from it - a sense of power, of domination, of control. And they will murder millions.
The Bible claims that Pride (what the Greeks called Hubris) is the worst sin of all and the basis of all the rest.
So, then, our self-consciousness, and our Pride, is the root of our problems. When you have that kind of Pride/Hubris, you think you are always right, and those who disagree with you are always wrong. Being wrong, they are evil, and so can be safely killed.
Obviously, we can't stop being self-conscious. We wouldn't be human anymore - we'd be the Borg, who don't have any self-consciousness, and so don't have any concept of good and evil.
These days, it's known the basis of our Pride/Hubris is our narcissism - splitting everything into good and bad with nothing in-between. We're born with this narcissism, which is why the concept of "Orginal Sin" exists.
Are animals narcissistic? I don't know - they're not self-conscious. If dogs and cats were self-conscious, would they make large-scale wars on each other? I don't know. No one knows.
If animals were self-conscious, and knew "good and evil," all of us would probably be at war with each other to the extent we'd have rid the world of them, or they of us.
I'll have to admit that while I like people individually, I don't particularly like the human race. How can anymore like beings that appear to be insane and have dealt such death and destruction to its own kind - and enjoyed it?
It's as if the human race is permanently three years old - physically grown up and grown strong, but ethically? That's a different story. Weaklings.