This week, in service of determining the true origin of Oikura Sodachi’s intense hatred of him, Araragi dutifully tells Ougi the story of summer break five years ago, when he was in the seventh grade and struggling at math. The envelopes in his shoe locker led him to the mansion where a mysterious girl would teach him not just math, but to like and even love math.
The girl eventually came up with three conditions Araragi had to agree with: the lessons would only take place in that specific room (where Araragi and Ougi presently stand); the lessons must be kept a secret between the two of them, and he must make no effort to find out more about her, or discuss anything not about mathmatics, or even ask her her name.
Following her conditions, Araragi had a great time, and the girl seemed to as well. In fact, as Araragi states, he was “created” that summer; that is, the Araragi his is today is thanks in large part to that girl getting him back on the right track with math, allowing him to continue living the happy, righteous life he now lives rather than having to deal with the repercussions of increasingly dropping grades. In other words, whatever the reason she disappeared, Araragi owes her.
After his story, Ougi figures out quite quickly (she is a great sleuth) two things that never occured to Araragi, and blow this hatred investigation wide open. First: the mysterious “math fairy” that “created” him was most likely Oikura Sodachi, meaning Araragi met her, and she performed a life-changing service for him, years before he thought he first met her.
The reason she never told Araragi this is Ougi’s second conclusion: Araragi wasn’t a guy she could count on. Young Araragi was so happy to be absorbing all of Sodachi’s mathematical knowledge, he neither thought much of her strange, specific conditions, nor the conditions of the home, which he wrongly remembers being in ruins. In reality, five years ago the mansion was Sodachi’s house, but it was a house falling apart, probably due to domestic abuse.
Sodachi invited Araragi to her house again and again in hopes he’d see the state of affairs there and relay the situation to his parents, police officers/champions of justice both. But he didn’t. And when Summer ended, Sodachi and her family disappeared, all Araragi found was an empty envelope, which he didn’t understand until now, when Ougi is drawing it all out for him: the envelope is him: “empty and disappointing.”
That’s why Sodachi despises Araragi. Becoming aware of the true nature of his past and what he did or rather didn’t do, Araragi also comes to depsise himself a little bit, for which Ougi has an intriguing response: that she’ll love him that exact same “little bit”…perhaps out of a desire to maintain balance?
Yet despite Sodachi despising him and despising himself a little, he still loves mathematics. Even if he misinterpreted the purpose of his study sessions with Sodachi, they still imbued him with a formidable love of math, almost like a “curse.” And now that he knows what he most likely did to Sodachi, he’s more nervous about confronting her and a simple apology may not be sufficient.
Enter Tsubasa, who throws another wrinkle into Araragi and Ougi’s supposedly solved proof: Araragi kept the occupation of his parents a closely-guarded secret. So how did Sodachi find out? The answer to that question, and how Araragi’s next encounter with Sodachi will go (assuming he has one), comprises ample material for next week’s outing.