Dragan,
I know you didn't say it, but I don't see how we can be both "intrinsically moral" and still need to develop morality through nurturing, training or a lifetime of striving.
If you say that it is society that sets morality, then the fact that some societies decline quickly into corruption and barbarism indicates they had it "wrong".
Which does tend to indicate that "morality" and stability have an intrinsic "rightness" or value which is independent of what any human grouping might think. History shows that selecting a tried-and-true morality gives a better result. If it is community benefit that motivates us, we cannot afford to ignore this point, no matter how much we may disagree with some aspects of it.
Have you read "Lord of the Flies"?
"... They ne'er cared for us
yet: suffer us to famish, and their store-houses
crammed with grain; make edicts for usury, to
support usurers; repeal daily any wholesome act
established against the rich, and provide more
piercing statutes daily, to chain up and restrain
the poor. If the wars eat us not up, they will; and
there's all the love they bear us."
-- Shakespeare: Coriolanus, Act 1, scene 1
