not a mistranslation. in some countries including korea, sometimes you dont get privileges as a family/a hetero couple do (e.g if one get hospitalized, only family / partner can see them. if youre in a same sex rs, this doesnt apply). you also cant get married to your same sex partner so adoption is a loophole people use to still have that privileges and be together.
kwon cant be a co-parent bc thats not a thing in the system. thats equal to a spouse. so it was either kwon adopt ho and sol or ho adopt kwon.
(pls correct me if im wrong this is just stuff i read online)

I’m confused I thought Mr Kwon adopted Sol as like a second parent, not adopted Ho??? Why would he adopt his boyfriend bro, is this just a mistranslation?