It always baffles me when countries don't allow for same sex couples to adopt. There's so many kids out there that need loving parents and a good home.
It mainly has to do how marriage works in Japan and how slow they are with changing the system. For marriage the woman has to be registered into the man's family register which is why same-sex couples cannot do that right now. Single mothers are generally looked down upon, and up until not too long ago children born out of wedlock did not have the same rights as "regular" kids when it would come to things such as inheritance.
Japan's adoption system is pretty bad anyway, only around 15% of orphans in childcare institutions actually get adopted (compared to something like 70+% of the UK and the US). Additionally, most adoptions in Japan are adult men getting adopted into families so the family can keep their family name and company through their adopted heir. Ironically this also allows same-sex couples to become recognized as family by adopting the other.