I'm pretty sure that Yuki and Shido like each other. However, Yuki thinks that Shido likes Kaga but decides to use that as a way of spending time with her. Shido probably takes advantage of the misunderstanding as well to spend more time with Yuki. Kaga is... just there. Shido gets jealous of Kaga and believes that Yuki likes Kaga which is why she told Yuki, "Besides, you wouldn't like it if I gave that letter to her, would you?" Which just strings along the misconceptions >__<
I think it'd make more sense if we had a glimpse of them before all this letter business went down/