...a behavior is "right" if it's beneficial to the species' survival and prosperity, and "wrong" if harmful to the species...
Great insight, very close. There is no need to cut along species lines.
A behavior is "right" if it helps carry the greatest amount of your genes (or the genes most similar to yours) into the next generation.
Like giving up your life for your kids, but maybe not for your grandparents.
Not risking your life to try to save a mouse.
Feeling free to eat vegetables but maybe not other mammals.
It's funny how people who want to "save the baby seals" are perfectly fine taking antibiotics and anti-virals.
They are both just as 'alive'.
We have more empathy for people and animals who's DNA is more similar to our own.
(Disclaimer: I gleaned all these insights from reading Dawkins. I wasn't smart enough to come up with them on my own.)