Um most of what's happening here doesn't require them to seek therapy. Maybe yahwi as he does have past trauma but Jooin and Cain? Nah, more like they need to learn how communicate.
Cain with Jooin but with Jooin alone, he doesn't necessarily have to communicate with Cain but with at least with someone.
I think Jooin also needs some sessions, because maybe he doesn't have a dark and tragic past like Yahwi, but his relationship with him has been quite stormy and he has suffered a lot for it. Obviously, the lack of communication is also a big issue here, but that is THE FACTOR allowing this story to continue lengthening (as happens with many others in which their authors don't know how to keep going).
This ain't westerners where it's so easy to go to therapy plus the author is Korean, and you know what? Discussing mental health concerns is considered taboo in many Asian cultures, If you admit you need help for your mental health, parents and other family members might experience fear and shame. As a result they tend to ignore, dismiss and nefglect this kind of mental issues.
Bro thinks he's a reincarnated dog but doesn't need help?
I know, dear. That's exactly why I would think it would be great if they started developing that theme in their stories. Addressing it in fiction could make many readers see that this option exists, it's not humiliating and maybe can help them see beyond, as the issue of bullying has been addressed, for example.
I hope one day, not too far away, all those authors of toxic manwhas will seriously consider the possibility of sending their characters to therapy. It would be really good for the narrative and the character development, honestly. I know too several of us here are drama lovers, but I think there are limits to everything... But that's just my thought