I think it's a valid question, one I was thinking about asking, but I couldn't think about doing it in both a respectful and direct manner. I'd imagine that Japan is going to be much more accepting of homosexuality soon, if you look at some of the culture trends that I've been hearing about. (I don't live there, so this is second hand.) Part of the reason that the Japanese population is declining is because of the males acting more (stereotypical) female than is expected, and visa versa. Thus, females would normally want a more aggressive man and and the males want a more understanding female. This is not true overall from what I hear, just a culture phenomena in the majority. An easy explanation would be that the "gender"chemicals are in different distributions.
In breif: The males may be receiving more estrogen
and the females may be receiving more testosterone
, which may be linked to homosexuality if a person has more of the opposite gender's hormone during pregnancy (more of that chemical in the womb, etc.)
Thus the voting pool may be more and more homosexual as the years roll by.
Okay, that topic aside, I think that the wikipedia articles Brythian linked (hat tip for that) show that Japan may be slightly discriminatory against same-sex legally (age of consent is different, wording of the law) we must also understand that Japan is a very old country. America has some similar issues in its constitution because it was written by slave owners who don't live in the 2000's where gay rights are an issue rather than states rights. However, popular culture seems to mark it a non-issue (Transgender Politician in 2003, politician "coming out" during residency in 2005, Politician who was openly gay elected in 2011, media icons who are openly homosexual [Although mostly gay].
So I'd think the answer would depend heavily on her family, but if I had to guess, it would've been only a partial reason, and if it was, it was made by Misha herself, rather than family forcing her. Of course, that is assuming about a fictional character based on an outsider's limited research to the matter. Now, I have often wondered if it is possible to attend Yamaku without a disability, but I think you can looking at some of the dialogue in the game.
Edit: Just played Lilly's route for a bit, you can attend without a disability.
This is all outsider speculation made by a layman on all topics, so I'd love to be proven wrong, or right, by someone with more experience and learning on the matter.
KeiichiO: America's much bigger than Japan, and we were still discriminating against 50%
of the population until 1920, which makes us less than 100 years legally tolerant, to say nothing of the social issues still lingering on the subject. So it isn't unheard of for a very minor majority (2-5 people in a family by American standards) to be willing to do such a thing to a child. If it's possible to go with Yamaku without a clinical disability, then if her parents felt it was best for her to go there, then she could be sent there. But that's just my speculation on the matter.
Just for an extra pip of information, Japan granted female voting rights 26 years
after America did, so that may provide some framing for my comment about America.