I’d tread carefully and request some elaboration from him on the situation because just based on what he said that could be all over the place, and I’m not too familiar with the culture and laws in South Korea so you’re probably going to want to do some research on their divorce laws and how their culture views divorce.

This could be anything from he’s cheating to to they’re both living totally separate lives, have agreed their marriage is over and just haven’t done the paperwork to make it official for any number of reasons.

Off the top of my head, in no particular order here’s a couple plausible-sounding scenarios, and it’s not meant to be an exhaustive list.

He could be straight-up cheating and lying through his teeth to you.

Maybe he’s even hoping to be caught cheating because he wants to get divorced and his wife doesn’t and he’s trying to goad her into it because it’s in some way advantageous for him if she’s the one who files for it. Maybe it gives him some kind of legal leverage to not be the one filing for it, maybe he just wants to be able to spin it as being her fault so he can claim to their friends or family that he was willing to work on their marriage and she wasn’t.

It could be that they’re totally on the same page, have agreed to see other people, and are staying together on paper because there’s tax incentives for married couples, or wonky inheritance laws at play and by staying “married” it’s easier for them to make sure the other spouse can inherit their assets to help take care of their son if something happens to one of them.

Or maybe they just haven’t had the time or money to money to do the paperwork and just don’t feel like it’s a pressing issue right now.

Maybe they don’t want to saddle their son with dealing with the fallout of a potentially messy divorce until he’s older, either due to legal/financial reasons, or because of some kind of social stigma.

Maybe he’s not even in contact with his wife and they haven’t seen or spoken to each other in years, and it’s just a pain in the ass to track each other down so that papers can be served, or they just really don’t want to have contact with each other and are avoiding it until there’s a real need like if one of them wants to remarry (I’ve known a couple people in similar situations in the US)

Again, I’d say try to push him for more details, it can be a touchy subject for a lot of people and he may not want to air all of his and his wife’s dirty laundry to someone he just met, and that’s understandable, but you also should be allowed to understand what kind of situation you’re getting yourself into. Find out if his wife is aware of it, confirm with her directly if possible. If he won’t let you talk to her to confirm that could be a red flag that he’s cheating, but it could also be that she’s unstable and it’s really better to not talk to her and risk her getting aggressive towards him, you, or their son, so tread carefully. Trust, but verify. There could be a whole novel squeezed in between the lines here that you need to be reading.