I think I remember that Hiiragi hates Tsubaki 'cause she thinks Tsubaki's better than her. Since Tsubaki looks down on herself, Hiiragi is pissed since that makes her even worse or whatever. Wait, and then Tsubaki hates herself since Hiiragi hates her? But Hiiragi starts hating her because Tsubaki hates herself?
So, you're basically right referring to the reason why Hiiragi dislikes Tsubaki. Just like any siblings, there's the moment where one of them excels a lot better at everything they do which is Tsubaki in this situation while Hiiragi is being left in her shadow. Like you said Hiiragi doesn't like the fact that even though Tsubaki is good at everything she fails to appreciate herself. Therefore since they're twins it's like Tsubaki doesn't respect or like Hiiragi because they share the "same face". It's confusing to put in words because of the concept but if you reread the chapters that explain it you'll understand better.