Finished watching episode 2+3 of
Owarimonogatari which covers the arc
Sodachi Riddle.
As we learned at the end of episode 1 of Owarimonogatari, Oikura has come back to school. Her attitude towards Koyomi is very much the same as it was before she left two years ago. The problem is that he doesn't know why she hates him. Normally, if someone hates you, you would have a good idea why. Essentially, she seems to hate him with the resolve that he killed her parents.
She mentions his justice is self-righteous. Meaning he naively believes he has done nothing wrong. To try to solve this issue, Koyomi takes Ougi back to when he visited a ruined house where he got tutored by a girl when he was in 7th grade.
Koyomi struggled with mathematics at a young age. So he was led to this ruined house to be tutored by a girl his age. This experience was more than just getting tutored in math, he enjoyed his time with that girl. HE came to love math as the time he spent here was closer to hanging out with a friend rather than a study session. By loving mathematics, he came to find the world more interesting. Which ultimately inspired him to be the person he is today.
Now we trace the attitude Oikura has right now. Essentially, she meant Koyomi is who he is because of her. As Koyomi is rather helpless, he is unable to make the connection that girl and Oikura are one and the same. She was targeting Koyomi from the start. She was aiming Koyomi to come not to an abandoned house, but rather to her home. After all, whenever they had a meeting, she was always there first. The only time Koyomi arrived first is when the girl never showed up.
But this raises the question of why would Oikura's home be in the state it was in? Simply put, she was raised in a bad environment with terrible parents. Now this goes back to Koyomi and what Oikura declares him being self-righteous. She was more than likely being abused and there were clear signs of it, but Koyomi never picked it up. Essentially, she is a girl who needed help, but never received it. From Koyomi's perspective, he was both naive and an idiot. From Oikura's perspective, it seemed like his thought process was more in the line of, well, this isn't my issue, and she assumed he ignored her signs of help.
Well, you ask why would Oikura go after Koyomi? What can a kid the same age as her do to help her from abusive parents? That is because both of his parents are police officers. All he had to was mention to his parents of Oikura's living conditions. The police would investigate and, more than likely, the parents would be punished. But that never happened. Which is why Oikura thought that she ignored him.
What makes this even more tragic from Oikura's end was that she thought bringing this boy with parents as police officers could have saved me. Which is why when they met up, she didn't want compensation. She assumed that the compensation that she would receive is the police's help. It is hard for a child being abused to ask for help. But nothing happened.
There was one session that they had that ended early. Given the massive clue of her being abused by her parents, Koyomi was more than likely in the position to clearly see her parents abusing her. Given the next day, nothing happened. She left was never seen again. All that was left was the empty note.
The time spent with Oikura was a life-changing event for him. It changed the person who he was, but for Koyomi he received all the help and knowledge from Oikura, but he gave nothing in return. The invitation symbolizes the knowledge that Oikura gave him. While the final letter that he read after Oikura left was empty. This symbolizes the amount of help he gave her. Which was nothing, absolutely empty.
Overall, this really clears up why Oikura had so much hatred for Koyomi in the flashback from the Ogi Formula arc, making so much sense. She gave him her knowledge of math and not only did he not help her, but he surpassed her in the subject that she loved. Though it does bring the question of how Oikura knew Koyomi's parents were police officers. As Hanekawa mentions, it is more than likely there is more that Koyomi doesn't remember. Or perhaps doesn't want to remember regarding Oikura.
Regardless, this was a fantastic arc that really used the elements from the previous one so well.