The only explanation I can come up with regarding Touya and Kira fighting, is simply jealousy. There's hints of it in the show when Kira felt he could be a knight too, and Touya goes and says it isn't easy and not everyone can be a knight. Kira obviously wasn't going to listen to that and kept training. Perhaps the scene was to show that he could be as good as Touya perhaps better. I'm trying to remember the end of the show, but I thought at one point Kira was actually the hero knight, not Touya, even though all along it was touted that Touya was the hero.
Any pictures of the animaloids to compare?