The closest we ever get is that line in the main story about how Rio thinks of relationships between women as being inherently adversarial which is a FASCINATING psychological snarl to give a character but nothing about it is ever fleshed out and, so far at least, we've seen nothing to indicate why she believes that or how it influences her behaviour.
I think this is all below the surface. Rio likes to brag, show off, and feed her ego. I still think about the cookies/pastries she did last chapter, and how the author declared at the end with a comment about "an attack" or such. The best I can think of is that it has to do something about "feminity" and the Japanese culture values about women.
Like, I don't think she thinks highly of her friends, at all. Not in their adulthood... not even in their college years.
From what Mahoro tells us in the main story, Rio was the "wise one", the "onee-san", the "one with a neutral voice"... but... was all of it honest? An act? Because, the author portrayed Mahoro and the others in college much more like: "plain and not exactly smart" Mahoro, "the one that sleeps around" Momoka, and "ugly and try-hard" Kyouko (I mean, didn't we all think it was Momoka who was having sex with Rei, at first? Up until the first twist, anyway?). So, what is exactly the reason Rio still was 'friends' with them? To boost her ego and superiority? "
I'm not like them, at all. I'm so much better".
And it's like... she married a "cute" guy, she is well-off, she is even an entrepreneur at the side! What do the other have compared to her? Maybe she thinks like: "Momoka, who slept around, is single and unmarried". "Kyouko got married, yes, and has a kid... but her sex life is nonexistent!", and Mahoro... "she says that she is happy, but Rei says she is lazy, she is unfit as a wife and DOESN'T even look at her as a woman. What nonsense!". "
I'm not like them, at all. I'm so much better...
right?" Especially because she isn't truly happy with Itsuki... but what the hell! She doesn't want to divorce (I don't think Itsuki would like it as an option either, tbh?), because she would lose her stability, and doesn't want to be seen as a divorced woman, either. "
Yeah, I will show them! I will show them I'm DEFINITELY better than them!"
So, I imagine that as an adult her beliefs about "friendship between women is just an illusion", are just because she feels women are always comparing themselves between each other. Someone has to "win". "To have it better than the other(s)" and such. Something that started as a "friendship", in her head, isn't honest and has ulterior motives for feeling superior later on life (that is if they are still friends later on).
I do agree that I feel like this whole "friendship between women is just an illusion" angle would have been better to explore and illustrate in this spin-off? Like, showing us up much more about why she thinks it like that. Comparing herself to the others (and not just Mahoro). I know we are still early (in her POV) before the actual letter she left and provoking Kyouko to "go and get Rei for herself", but... I would have liked to see how she does, in fact, think about her supposedly friends. Although it all feel implicit.
