Dang, what with the hate on Hiiragi ? What she does is pretty understandable. Imagine having your twin who always relied on you suddendly becoming better than you at everything but still thinking she is worthless without you. Hiiragi is just angry that her sister can't realize how good she is and instead insist on puttting herself down. Imagine how frustrating that is, having someone who is better than you but insisting on telling she is bad, it's extremlyfrustrating.
Leaving aside the issue that all of this mess could have been avoided if Hiiragi had had the guts to say a single sentence about her plans or her feelings to Tsubaki...
You may not realize this, but high schools in Japan are a big deal. They can have a huge impact on your acceptance into a prestigious university, which in turn will have a huge impact on your job prospects (much larger than how well you actually study at that university). By refusing to simply tell Tsubaki that she wanted to go to a different high school, and thereby letting her deliberately downgrade to a lesser school than the one she wanted, Hiiragi may have damaged Tsubaki's future prospects very badly out of nothing but petty spite and insecurity. In Tsubaki's position, I'm not sure I could ever forgive that.
Also, this is making me hate Hiiragi a great deal indeed, but objectively their parents are even worse. It was their responsibility to step in and clarify the situation when Tsubaki turned down her first choice of high school under the impression that she would be going to the same place as Hiiragi. They knew Hiiragi's plans. They have failed their daughters quite thoroughly.