Shizuku is dying, isn’t she? She always had a crush on Riku, but Takt confessed to her first and, to not create any issues between the friends, she ended up going out with Takt. Takt also has something for Riku, so he keeps trying to keep anyone from getting closer to Riku.
Thing is, Shizuku is dying/moving away/vanishing out of thin air and now is hellbent on being with Riku, but Takt knows something and is using this info to keep her at bay. Either that, or she’s with Takt for some family reason (Takt family is loaded and controlling) and after graduating they will move away and break contact with Riku.
Or the story is shite and nothing makes sense, with stuff hacked together just to create some suspense.