愛さずにいられない。

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Rinha sees her older sister, Kaya Kei, who retired as an idol way too early on in Saki so much that she became a huge fan of Saki and even calls her Onee-chan in Ume's story. This mention of her sister is only in Saki's step 2 CMIIW, in Ume's there's hints but not much.

Thus, Rinha ALSO projects herself in Ume--- the extremely talented little sister who seemingly always lost against her sister but have brooding talent that causes fear towards the older sister of being surpassed, which explains why she immediately pulls an antagonistic attitude towards Ume in general and teases her by trying to take Saki's sisterly affection away from her during her Step 2.

At the midst of Ume's step 2, Rinha lost against Ume and said that since she wants to quit being an idol anyway she could trust her fans to Ume instead. (spoilers for step 3; she ends up preparing herself on coming back as an idol and ONLY telling Ume about it so far. I know what you are, Rinha)

Misuzu mentions she gets along well with Ume because Ume reminds her of who Rinha used to be. Judging from a few lines where Rinha introduces herself to Temari in her stories, it's very possible that Kei's idol retirement caused Rinha to be the bitter girl we know as for today and that she used to be a cheerful girl like Ume is.

THUS, Rinha and Ume's parallels are very strong while they ALSO fits the 'sunshine x grumpy' dynamic. Except the grumpy used to be a sunshine too I guess.

But in some ways; they're also different. Rinha asked in Ume's step 3 story that what would she do if Saki's light 'burned out' but Ume trusts Saki too much and vice versa that she knew they would be fine in any case, that Rinha feels bitter about it (pictured in the screenshot)