Kurata is the yandere to Misao from Misao. Major spoilers up ahead.
He was bullied when he was in high school, being mocked for his appearance. One day, a girl named Takano started hanging out with him to drive away the bullies. This resulted in him forming a crush on her. His affections grew and grew, until one day, he decided to confess. His confession turned into an assault after Takano rejected him. He strangled her, but a teacher came and stopped him. Takano stopped talking to him after that.
Kurata is very sensitive when he hears people talk about his appearance. He hates is so much because his classmates focused more on what he looked like rather than who he was. Thinking that people would accept him, he had undergone plastic surgery. He's also very sensitive to rejection, which was also something that happened a lot in high school. Things only amplified when Takano, a girl he started developing feelings for, rejected his confession and admitted that her association with him was out of pity. This carried over into his adult years when he killed Misao, one of his students, for rejecting his romantic advances. After he disposed of her body, he kept Misao's hands with him as a souvenir of her. Should he not be killed by Aki/Akito, he will pursue another female student.