None wrong with her. She just had a very hard choice to make, And wanted the best for both of her kids, despite his homophobia he is still her child.
We can't really understand that decision ofc.
But I think she did her best, she decided to take advantage of the maturity and good nature of the little brother and made him independent faster and
As she indicated the big brother having independence would have gone bad.
Everything is wrong with her, that choice she decided to make is in no way valid. Kicking out an underage victim of homophobia after he decided to fight back because of all the harassment he received is not how a parent should do. That sent a wrong message. And don't forget that she guilttriped and manipulated him in the process into agreeing with her, eventually forcing him to bear her fault for failing to educate the older brother. This is after she did nothing to protect Woojin from being targeted by the delinquents because of the brother. Sure, she supported Woojin financially and offered words of comfort, but that's about it.
Also, "the big brother having independence would have gone bad"? That's an ADULT, mind you. Of course he would and SHOULD be independent. Society is the best teacher to knock some sense into him, this is called consequences, and he needs to learn that not everything should go his way
That doesn't end there, though. She also told him to attend the wedding of the one who harassed him after he decided to cut off the toxic mf out of his life. That's pretty shitty, to be honest. I just hope the brother won't do something as low as making homophobia remarks and making Woojin feel small in front of the guests at the wedding

Really make me like the mom on the previous chapter only to make hate her REAL BAD this one. Wtf is wrong with her???