The way Jesus wanted people to act towards each other seems counter to the very human nature you think is unchangeable, though.
There are a lot of verses in this link, for example, that you seem to be arguing are exhorting people to act against human nature:
What does the Bible say about Selfishness? Scripture offers profound wisdom on the topic of selfishness. We are warned of the temptation and perils of being selfish rather than generous and helpful to our family and neighbors.
www.biblestudytools.com
I think the teaching of these verses to people for thousands of years as the gospel has inculcated people to believe they should act unselfishly more than before they were taught. I think the notion has so permeated society (nearly all of them, now, even the non-Christian ones) that it really has changed how people think and act. Note I'm focused on actions, not urges or instincts. And I think that if we changed, and had a society teaching for thousands of years that one should only act selfishly, then far less actions that we now consider unselfish would occur.