As someone who also has a fairly big inferiority complex... gods I relate to Kurokawa a lot here. I'm sorry, but something as deep seated as that, something that's been with you since childhood, isn't something you're gonna be able to get over by just being friends(?) with a pretty girl for a few weeks(months? Forget how long it's been in manga), but something you honestly need proper professional help with. Remember why she didn't want them calling each other by their first names? Cause they're not equal. At least to Kurokawa they aren't.
Let me put this in perspective: you don't like yourself. People have put you down throughout your entire life to the point you're doing it yourself. Then you meet a person who you consider radiant. You put them on a pedestal, admiring them from afar. For you that's enough, that's all you think you're worthy of. You might become friends with them, talk to them, but they're still on that pedestal, still standing above you. But you understand that, you're okay with that. Then, all of a sudden (to you anyway) the person tries to pull you up, confessing that they love you. You can't comprehend it, you WON'T. To be able to love another you have to be on equal footing, to be able to look them in the eye. This person confessing to you implies that you're equal, but you know better. You're not equal, and you never will be. So you push them away, because you believe they're better than you, too good for you.
Sound familiar? I've a feeling this is the sorta thing Kurokawa is going through. And the kicker? Nanaki herself (though she regrets it now) helped enforce that mindset, Miki as well. So when Izumi tells an obviously stricken/depressed Kurokawa to consider NANAKI'S feelings before her own? And adding to the fact that to Kurokawa Izumi is above her, on equal footing with Nanaki? It's no wonder she snapped.
As painful as it's gonna be to see Miki chew out Kurokawa... I think she's gonna need it to be able to stand up and talk to Nanaki about things.
tl;dr I really feel and understand what Kurokawa's going through and really hope she can learn to love herself so she can love Nanaki and get some professional help cause god damn she needs and deserves it