I mean i get that explanation too, I just felt like with the way she tried to look like her boyfriend a few chapters before that I interpreted it more as people thinking I'm dating a guy than dating a guy itself. But not like it's that big of a difference
Also, yeah, going back to that for a moment, Asuna was actively willing to do whatever just to spend some more time with her girlfriend, even if it meant crossdressing to do it, and Misono shut her down. It's a conflict that really symbolizes their differences in openness, as Misono didn't care for it and just wanted to be dating Asuna, meanwhile Misono was beginning to feel lonely and disheartened that they couldn't do anything normal couples could due to Asuna's reasonable yet overbearing fear of being "different". Misono seems satisfied with the fact that she's finally "dating" another girl after forcing herself to date a boy to seem "normal", and Asuna wants to actually take part in the kind of acts that couples would actually do.
They're both afraid of being outed, with Misono scared that her friends would hate her, but she's still trying her best. They end up in different classes and can't spend much time together, so Misono waits outside Asuna's cram school so they can at least spend some time together. Asuna doesn't want to be seen with her in public, so Misono crossdresses. Each and every time though, Asuna's insistence on not standing out essentially tramples over Misono's efforts, so it's no wonder that she's gotten so irritated. It's never been a healthy relationship, with it starting from Asuna essentially using Misono as an outlet for her lust while stuck in a loveless relationship with a boy she didn't have feelings for, but I hate how Asuna wanting to have some semblance of a relationship is always portrayed so negatively. If they can only be a couple in private, then the 99% of time where they're in public probably makes Misono feel utterly forgotten and unimportant, but we're made to feel like Asuna, the girl who toyed with her heart for months, is the victim in all of this. Asuna shouldn't get a pass, especially with how "smart" she's made out to be. She's constantly hearing about Misono's problems, and doing nothing about it besides essentially telling her to suck it up, and not making any efforts to say anything like "hey, I know we're busy right now, but how about we take a train an hour away and spend our next day off together where nobody we know will see us."
Honestly, they do really need space from each other, but I feel like the time apart is only going to be used to make Misono even more miserable, so she'll have to bottle up even more about herself just to get Asuna to continue their theoretical relationship. There's no hope for them to stay together after high school considering Asuna is in the top class and constantly studying while her girlfriend is spending her time waiting for her, so I almost wish they stay apart, but I know they're going to be brought back into the same dysfunctional relationship so that the author can milk it long past its time of death.