Japan is extremely conservative in certain ways, usually because of their focus on conformance to social norms.

I encountered gay men not-infrequently while I lived there, and Japanese people are (for the most part) fine with them even if uncomfortable, but from a legal standpoint, Japan mostly prefers to pretend the LGBT+ community doesn't exist, and can be very hostile towards it when it's forced to acknowledge them (such as in medical contexts).

Why was there this law in the first place?

In Europe at least, it was often explained as "same-sex marriage and parenthood are not allowed, and a legal gender change cannot be a loophole to that". But it appears to be a post-hoc rationalisation since the forced sterilisation programmes have many more targets in the past until it was progressively abandoned for more and more groups. It was also becoming untenable since more and more countries were legalising same-sex parenthood.

So, if we are being more honest, it's eugenics.