Adding to what Cornonthekopp said about the theme of "S vs Yuri", I think there's another important theme: can an artificial relationship work? Can a relationship where both people are pretending come to any good, or will it only result in harm?
Every relationship in this story started by patterning on fictional relationships: Hanamonogatari for everyone except Yamabe and Mia, who made up their own Desk Ghost story. Of the four relationships so far, we can divide them into two categories (using the jargon developed in this thread):
Sunflowers: Kasumi & Haruyo, Yamabe & Mia
Box cutters: Sayori & Mizuki, Aoyama & Yurika
What I've noticed is that the happier relationships have aspects that explicitly marked the role play aspects as such. Kasumi and Haruyo switch ribbons and speaking styles when engaging in the "S" relationship. Yamabe and Mia converse in letters to and from a ghost. There's no mistaking where the pretend relationship ends and the real relationship begins. The aquarium date has both Kasumi and Haruyo out of character and out of costume, so they can speak to each other as themselves and know this isn't part of the game. Haruyo even talks about why she plays the Onee-san role. It also helps that Haruyo is actually the younger one, so the Older/Younger Sister dynamic is consciously manufactured by both of them.
This is similar to how actors in a play can have fake emotions and fake relationships night after night and not be hurt when the play ends. What happens onstage is not real, so the emotions and relationships can be left behind when offstage.
The other advantage of having explicit boundaries around the pretend part is that it allows for renegotiating the relationship, as in Yamabe and Mia's relationship once they meet again. Even if Mia was annoyed that they never met in school, their reconnection was still a happy occasion because neither of them were hurt when the pretend relationship ended.
The box cutter pairs had no such boundaries. Well, Sayori and Mizuki, certainly didn't. I'm predicting this will also be the case for Aoyama and Yurika.
Though, Sayori and Mizuki may have started by explicitly calling their relationship "S", it didn't stay that way. They acted like lovers all the time, from secret waves at school to more physical intimacy. There was no separation between "onstage" and "offstage" behavior. When Mizuki said she was looking for 2-person apartments, Sayori was surprised since she expected this game to end at graduation. It wasn't supposed to be a real relationship, and she wasn't going to let a game stop her from going to the college she wanted to go to. Mizuki thought it was a real relationship, and put up with her hardships at college on the expectation that her girlfriend would join her. This mismatch caused expectations to be unmet, which led to the violence.
The danger of a pretend relationship is that, without explicit boundaries, pretend feelings can quickly become real. If that doesn't happen for both people at the same time, somebody's going to get hurt.
