(I'm not Korean, but I've lived there for some years, can communicate in the language and read the news, and am married to a South Korean citizen with a child on the way; the latter is one of the reasons we moved away.)
Care to explain precisely what you mean in this context? Because it's hard not to see this as a dog-whistle for "why can't women just be happy with the caretaker role?" but perhaps you mean something more benign.
Happy if Koreans could chime in.
Marriage rates in Korea are declining, as they are everywhere. But there is no evidence of increases in single men, other than in the uneducated and low-income group [1].
[1] https://www.straitstimes.com/asia/east-asia/poor-men-in-s-ko...
Korean men, I've no doubt.