That is a very good question. Im by no means an expert of this particular subject but I think it boils down to tradition and the general sentiment of marriage obviously having connotations of some sort of nuclear family and intergender relationship.

I am torn about the word marriage when it comes to homosexual marriage, not because I find it offensive, nor do I find it morally wrong for homosexuals to get married, but rather because the definition has traditionally implied a very obvious kind of relationship dynamic.

I think the problem in Japan will be very easily mitigated if there was a legal designation of a partner to be the beneficiary in the event there are other legal partner of whichever gender will receive benefits similar to that of a traditional marriages spouse.

Japan is very traditional oriented, which is ironic since the western convention of marriage is actually very foreign to Japan. In fact in Japan's Renaissance era in the 14th century, there was a term called "yobai" (night crawling) which means that if you crawled into someone's bed three nights in a row you are practically married by everyone's eyes. It's very foreign tell Western concept because there is no legal paperwork that denotes this, but socially it practically cemented idea that these people have a relationship that's more than just a mere fling.

Anyway bring it back to modern-day, I think that homosexuals definitely do not have all the same benefits of heterosexuals in Japan if you specifically talk about marriage, but I don't think Japan is really a country that sees things in a way where they have a entitlement complex to deserve everything they want.

Gaman is a Buddhist concept that I can very comfortably say almost every Japanese abides by, which means basically you're very capable of having a high tolerance toward bullshit.

There may be in fact a greater desire for homosexual to marry, but the combination of that Buddhist concept and the social lack of desire to cause ripples may be obscuring that.

But this is all my theory, I could be completely wrong about that.