Mai-HiME/Fridge

Fridge Brilliance

 * Fridge Brilliance can explain Shizuru's Psycho Lesbian phase. She doesn't become unhinged until after Nagi informs them all of the true nature of the Festival. Shizuru is pretty sharp. Her MIP is a HiME, as was she. She knew there was no way she could win. If she lost, Natsuki would vanish. If Natsuki lost, her MIP would vanish. Shizuru didn't know who Natsuki's MIP was, and given some of her statements, she had no reason to believe that it was herself. But she knew that if Natsuki lost, she would be deeply hurt by it. She was backed into a corner, and couldn't see a way out. Even suicide was out because Nagi had informed them all that killing yourself would instantly cause the death of your MIP.
 * In the Drama CD track "As the Cherry Blossoms Bloom," this is confirmed when it is revealed that Nagi approached her individually at some point after Episode 16, told her about the fate of the Himes, and said that she won't be able to hide any longer "because (her) beloved Natsuki-chan is not going to be able to escape this fate, either." Shizuru then realizes that her losing will cause Natsuki to vanish, but then wonders if Natsuki will one day accept her feelings.
 * So it makes sense for Shizuru to go insane when Nagi--who doesn't have the greatest track record for telling the truth to begin with, as a "sharp" person should easily notice--makes unfounded verbal threats, even though she didn't give a crap about Natsuki and managed to act completely rationally back when Alyssa was actually about to kill her with a proven Kill Sat? How does that even remotely work?