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Owarimonogatari, Ep 1
Ogi Formula.
This episode takes a step back and starts when Koyomi meets Ougi Oshino. Though at this point in the story, it is clear that she intentionally set up this meeting for another reason. Essentially, what was the reason that Koyomi changed as he entered high school and why he didn't want any friends. It had to do with an incident where a study group scored significantly higher than those that didn't on average. Here we are introduced to Sodachi Oikura, who held the class together to find the culprit. In many ways, she hated Koyomi because she scored higher than her on their respective math exams.
As the session turned into madness, Oikura decided that it was best to take a majority vote. In which it was not Koyomi surprising enough that was declared the suspect, but rather Oikura. Also, rather since that incident, she hasn't appeared in school. Despite her being the only one that voted that Koyomi was the suspect, the majority came on her. For someone as proud as Oikura, to have a reputation as a cheater must have been devastating.
What Ougi brings up is that nobody actually cheated. So if nobody cheated, where would you look their teacher? How does this add up to the study group? Essentially, their teacher used problems that the study group used. It wasn't that the study group had answers to the test in which they studied, but rather the teacher used that material to make the test. For the simple motivation that it would make her look good. Just on that alone makes her look sick.
But to make this situation somehow worse, the teacher was among those that voted. Which is something you wouldn't account for. Why would the teacher vote for the cheater? That would imply that they had a hunch. Why would the teacher not bring that up to the people's attention. It is because she wanted to make sure the blame didn't fall on her. I assume that when the students saw her vote for Oikura, more than likely that had a few of the other students feeling confirmed to go with her answer.
Just like the viewers, Koyomi was disgusted by the fact that a teacher, who is supposed to be a role model, could do something so unethical. Instead of earning a good assessment through effort, she took the easy way. By doing so, not only made 1 student suspected of stealing the answers. But pinning the blame on one of their students.
This is the reason why Koyomi attitude shifted to not wanting friends until he met Hanekawa. He saw not only the other students, but their teacher shifted the blame on Oikura. Making matters worse, Oikura determination to find the culprit and being the only one who voted that it was Koyomi set her up in the trap set up by the teacher. Koyomi per usually feeling the blame of if only I didn't score above her. This still lingers as he has never scored a perfect score on a math test since that day.
Now we aren't either alien with Ougi's suspect behavior. Why would she want Koyomi to tackle this answer? As Koyomi comes back the next day, Hanekawa mentions that Oikura has come back to school. Which is pretty big news. It seems that after they tackled the incident, the teacher went on maternity leave. Very interesting timing for Oikura to come back to school. Curious how events shift forward from here.