Doctrines don't scale
The reason we have intra-species conflict is because doctrines do not scale effectively
Each individual person has, as is common knowledge, a mental model of the world. This mental model, as is given, is flawed. It's almost certain that any one person cannot truly grasp the reasons behind the what, why, and how of our world. These differences in flawed mental models are what primarily cause conflicts, and have been the primary reason since the dawn of Homo sapiens.
One could see this and come to a conclusion: since these mental models lose their malleability as we grow older, it'd be in vain to do anything about changing them, and thus more effort must be put into conflict resolution and cooperation.
Here we come upon another realization (at least I did) that we have been doing conflict resolution and cooperation on an unprecedented scale since the start of the agricultural revolution, in the form of cities, kingdoms, empires, and nations. It was finally religion that eventually captured the most number of people, and today is the main driver behind cooperation across thousands of kilometers.
But for human conflict to be truly gone, we need one single belief, shared by the entire human species. As of this moment, I cannot think of one. (There are people who do not even believe in the Earth being round, so...) Even the most widespread doctrines cannot capture the entirety of the human population, not to mention effectively capture their minds (how many Christians are actually devoted?)
This means that as of now, our primary tool of communication, language (and humans), has yet to come up with a doctrine that can scale to nearly eight billion minds. We do not yet have one nation, one religion, nor one language.
I think the reason is the difference in evolution of the hardware (the anatomy of our body/brain) and the software (our mental models). Our minds developed complicated theories much faster than our primate brains could evolve, hence we still live like the forager bands roaming in the savannah: just that our bands have gotten bigger and intermingled.
In the future, I am optimistic that at least one such belief would spread, leading to a true unification (one could argue that the fear of nuclear weapons is one such thing, but you never know) of the human species.