also what I'm thinking is
Monobear is Syo, who has DID. This explains his erratic behavior and how he wants everyone to live in peace, while simultaneously wanting the students to kill each other to graduate. It also fits the white/black motive of the character design.
As for the case, book girl is acting strange because she had a loved one who was killed by Syo. Her famous book's "sailor" is actually her dead boyfriend.
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maybe, lol