So, the "origins" part of this may or may not be straightforward to some.
Allow me to explain. They do not state the beginnings of the events leading to Happy Wars explicitly in the game. They only state of two starkly opposite countries fighting in perpetual war, with no evidence of the end. They also state that they fight for reasons beyond anyone.
Here's my view on things. Three ancient houses prospered; one of the three grew in a lust of power (imperial power) and became the Dark-corps. The other two secured a very strong alliance and became the Lightish folk. Eventually, petty rivalries grew to minor battles, then to full-scale warfare.
Veering from the video-game point of Happy Wars and putting some thought into it, what is your Origins theory?