Aside from the fact that humans are significantly different than chimps in many ways, chimps rarely kill each other and have significant mechanisms for avoiding lethal interactions. The Gombe chimp war was an abomination that “shocked” Jane Goodall because it was such atypical behavior.
Unfortunately, patriarchal dominance hierarchies are now the vast majority of cultures, but in places like Denmark, empathy is taught in schools, children are encouraged to compete against their own prior performance and not against each other, and emotional intelligence is seen as very masculine. We need to start shifting our norms and the stories we tell that support them as well as to bring up children to see how interdependence and caring is actually personally beneficial (rather than every man for himself).
Certainly not an easy task — particularly since American-style capitalism is also domination-based, but since other Western democracies have moved in this direction (primarily in the Nordic countries), we could if we really wanted to.