I totally agree with you, especially considering the years of abuse Cheol has endured. Even in the present, he still struggles to confront his family. I don’t blame Minyoung for desperately wanting to take action, since Cheol’s situation keeps escalating every time, especially when he nearly died. However, I do think Minyoung’s approach is somewhat hasty, as you pointed out.
I think that was the straw that broke the camel’s back, so to speak. Eventually, Minyoung grew tired of what he saw as Cheol making "excuses" and decided to take matters into his own hands. His goal seemed to be forcing Cheol’s family to disown him, leaving Cheol with no choice but to separate himself from them. As we see in the present timeline, Cheol essentially ran away from his family.
Ultimately, I think that was Minyoung’s objective: if Cheol wasn’t going to cut his family out of his life himself, then he would make his family cut him out… by outing him.
I know that people hate that Cheol still obviously loves his family despite everything, but keep in mind that he has been in this abusive situation for most of his life. He’s stuck in a constant state of abuse and insecurity and it’s all he has ever really known and it’s not easy to just say f them - a part of him probably still wishes that they would just love him and care for him.
Minyoung is just too hasty - his uncle is totally right. He has no power, he doesn’t have any influence and even though he wishes he could, he can’t protect Cheol in the way he wants to. He wants to kill his family and then what? They’d run away together and go live in a fantasy where they never get caught?
I know this is fiction but even that has its limits lol