Did it start with Karin's private tutoring she left? Problems at her middle school? At home? Why was Karin so intent on getting into that college? Did she know someone who'd be going there? Did her family go there? We don't know. We'll never* know. It could have been anything or nothing and you'll never know. All it leaves is an emptiness that consumes everything with "why."
Here's a not so fun fact: today (the 1st of September) will be the deadliest day of the year for Japanese aged 10 to 19. This day is always the first day of the second school semester, and the youth and teen suicide rates see a massive surge at this time of year.
There exists one paramount reason: the "exam hell" of entrance exams are for a very limited number of academic slots. Unlike most western schools, where a fixed academic threshold is set, and admission is open to anyone who qualifies, entering elite Japanese schools are akin to making the roster of a sports team. Top schools are competitively pitted against each other in rankings for reasons of purely commercial and collective pride, and this can create very high standards for teachers and students alike.
But the cost is the trickle down of this competitive mindset into the classroom. To enter elite schools perfection is demanded, students are pitted against each other, and paranoia infects the student body. Bullying becomes a performative ritual with the intent of weeding out weaker competition. And there's the huge parental pressure to study and succeed, because academic success is seen as a reflection of parental quality and character, the local equivalent of "keeping up with the Joneses" and a source of both pride and derision. This is not merely academic accomplishment, it is Darwinian War, with victors and casualties, and often with lasting psychological trauma.