I suggest the nature of humans are seen in the behavior of the child. We have all seen children play and they are first and foremost about themselves and their possessions. So our nature is rather brutish. We have to train our children and ourselves to be more ethical and loving.
Over the last several years we have seen multiple videos of natural born "enemies" in the animal world who when raised together not only have no animosity towards each other but a down right "loving" relationship which seems to counter what we were taught as youngsters that yes indeed momma cheetah has to teach the kids to hunt but perhaps it is not natural at all that they want to kill the antelope, they were taught too.
I suppose that many humans still adore the war-like champion due to the inherent violent tendencies we have buried not so deep in our dark little cellar.
When it comes to ideas which we are taught, we often tend to presume too much the weight of the influence of teaching. I'm not saying children should be taught less, but that it should be individualized a lot more based on the natural traits which they exhibit, rather than the futile attempts which have been made to change less desired behaviors. For example, the idea that animals are born able to crawl, communicate, walk, run, and sometimes even climb on their day of birth, and since the human infant can do nothing but suck at a mother's breast, then it must be a "Blank Slate", whose future behaviors are entirely subject to environmental factors and teaching. Some groups really get up in arms and extremely irrational in shouting down any challenge to this idea, but the facts on genetic research have revealed strong evidence that human behavior is also (to at least some extent) genetically influenced. You cannot really mold a human mind like a piece of clay, some are naturally more inclined to take chances than others, some are naturally more inclined to be thoughtful, and others will be naturally more emotional.
Your example demonstrates that animals are not behaviorally ruled by the wisdom of instinct, they can learn to get along. Well of course they can, as do human children. If it takes humans more time, then it happens to be true that simpler animals are born with fully functioning brains, while the human newborn hasn't the hardware behind its eyes to see properly, nor the muscular control to do so much as roll over on its own. Of course all animals are born selfish, how could one not be when the only life form which it has ever known was itself while passing through the birth canal? Experience is the teacher of all living creatures, and it certainly takes experience for one to learn unselfishness.
Everything we learn takes experience, but some individuals may learn more of one trait than of others by the infuence of their genes, just as some may have blue eyes and others some other color. Education is an important means of focusing on desirable traits, but those who pretend it can make anyone the perfect servant, the perfect soldier, the perfect leader, or the perfect anything are foolish. When education is focused on the needs of the group instead of on bringing out the best in the individual, you will end up with a population similar to America as it now is. It isn't education which defines our human nature, it's our genes! Furthermore, these behavioral variances are distributed throughout all cultures and races, so I hope nobody's going to be like the shitheads who have called me a "racist" just for stating what is so plain to see. My experience is that those who angrily oppose any challenge to the supreme influence of education and upbringing are those who wish to wield god-like power over the human mind, because they are very angry and selfish people. I'm just trying to point out how the nature of each individual is itself individual. Remember, evolution never worked on any species, only the genes of individuals.