They are DEMONS, they are trying to exterminate us! We have to exterminate every last one of them before they get us!
If you look at history every war has dehumanized the opposition as much as possible to ensure the populace and army are willing enough to prosecute the war. Jews were likened to rats. America is easily depicted by extremists as a warmongering country that murders anyone in their path for resources like oil or if they feel threatened, giving the people who use this propaganda power over the people they tell it too. The best dehumanization is done with half-truths. And these demons arent called demons for nothing. This is either the most successful popaganda campaign or the demons really are all that violent (possibly because of the belief that humans are ultra-violent against them, which is pretty much the case).
With that information you can spin it several ways. Its a battle for survival. You are putting them out of their misery. You are exterminating them before they get enough demons together to exterminate you back. Its a religious right of passage to slay a demon giving you a lot of afterlife points. It is a sign of manlyhood or honor, like slaying a dragon or an enemy soldier is a valiant act.
Notice that you dont have to focus on the fate of the demon (who is hunted down). You can focus instead on the fate of the human(s) who do it: they can be heroes, just doing their duty, crusaders in a holy war or protectors of humanity.