It seems like the demon is attacking simply because she dislikes that the other side is handling a medical situation better than they are. I initially didn't think the demons would have anything to do with the weeds or the milk disease, but based on the demon girl's reaction to everything, it actually DOES seem like she attempted to poison and kill the people in the town with the weeds (unless they left the area).
I'm not sure what the deal is on her end, but so far she seems pretty scummy.
If neither side wants to fight why are they fighting? What are they fighting over?
Isn't that usually the case for war? Usually there isn't some cut-and-dry villain in a war. WWII may have had Nazi Germany and Japan, but WWI didn't really have anyone you could say was clearly in the right or wrong, both sides were just sort of caught up in a load of politics and military agreements that dragged everyone down and around.