I believe this is because Japan works under a civil law system, which means that case law is subordinate to written law. This means that courts have much less power to impose their decisions upon the executive. Thus I think it is because the Japanese legislature never passed a law which explicitly allows for same sex marriage, the executive is allowed to deny these unions.

However this is based on a very surface level understanding of legal systems and I am by no means an expert. I find the language surrounding legal systems to be very confusing.

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