Actually no. I would say that it is an expression of the best of human nature. But then (shock, horror), I don't believe in the divinity of the instructor!
That is part of why I describe myself as an atheist.
By 'nature' I did not mean
all things people do, but instead the natural instinctual impulses in us, what is sometimes called "the body".
People also do amazingly wonderful acts of kindness and generous aid to others, even self-sacrifice, from the thoughts of their minds, which include
learned ideas/ideals.
So, there we have 2 forces at least then: the instinctual and the learned.
"Nature and nurture", to use the old phrasing.
So, when I used the phrase "goes pasts human nature" I'm implicitly referring to
other forces in our minds (not innate, not natural), such as learned ideals.
Cultural ideas/ideals can of course be variously beneficial or harmful (there's quite a range of ideas), but many of the ideals are quite helpful and beneficial to civilization, civil society, peaceful coexistence.
Here's an example of a learned idea/ideal that is highly beneficial to society:
Matthew 7:12 In everything, then, do to others as you would have them do to you. For this is the essence of the Law and the Prophets.
To the extent the people of a nation follow this rule, just to that extent, the nation will be a good place to live.