Yeah, it was a weird battle. I could forgive Rin for not having any strategy at all since he's so hotheaded. But Yuki certainly is the intelligent type and I was expecting him to only ask Rin for assistance to get a diversion. Although looking at it from another point of view, having Rin first pester the demon with straightforward action could have been a simple tactic to make it hesitate when faced with Yuki's cold demeanour. If that was the case, and considering Yuki's personality, it's likely, then the whole thing went according to his plan.