So Naori shits on his feelings, makes fun of him, then Rumi asks him out, and somehow Rumi is the bad guy?
Even if she knew about Naori's feelings, and still loved MC and wanted to date him, that's fine, but what she's doing right now is enough to call her a piece of shit. She KNEW about Naori and MC's feelings, but ignored them and started dating MC, only to dump him after he truly fell in love with her, and tell him to date Naori? What the fuck? There's absolutely no way I'd honor her request.
There's an option that the two sister made some kind of shitty deal that Rumi gets to date MC for a year, and then it's Naori's turn. That would explain why she broke up with him on their anniversary.
That would align with Naori's metaphor from the previous chapter:
But that would make both sisters massive pieces of shit.