It’s the only way homosexual couples can become “married” in countries where it’s illegal. By having a direct family relationship they can have access to different things that they normally wouldn’t (for example if one gets in an accident and only family members are allowed in the hospital, they wouldn’t be able to do so without being in the same family registry.)
it's a way for queer couples to have legal protection and add each other as a next of kin when same sex marriage isn't legal - you don't hear about it much these days because a lot of countries in the west legalised same sex marriage but it used to happen a lot there too (but if you're in Asia, I've heard people still do that)

I don't know if I'm the only one confused by their family registration. Why is Ho registered as Haebom's child?