As a species, we do kill others and take their shit, as I already said. And this happens every single day. Sometimes it even happens on a very large scale.
The vast majority of people don't do that because we've built our societies to limit those tendencies, because that kind of violent chaos hurts the group.
You'll see the same thing throughout the animal kingdom. There may be fighting amongst different species (lions and hyenas, for example), and there may even be fighting amongst the same species (two prides of lions clashing), but social animals that form groups generally get along very well within those groups and don't murder each other randomly. It's common, because it provides an evolutionary advantage. Animals are stronger as a group.
Unfortunately for your point here, humans are actually the worst species on Earth when it comes to violence against their own species, and it's not even close.