Responses
It has already been explained in a previous chapter, the father had ordered to stop giving the mother medicine (or antidepressants) and Yeonho gave something that resembled the form of medicine that made the mother's condition worsen and she committed suicide.
That sentence refers to the fact that the son never wanted to blindly follow all his father's orders (as he himself said, to be his puppet)
Maybe the father used to argue like this with the mom and accidentally killed her. So he (and maybe yeonho father) hung her to cover the truth. (like he always said… he and his son is alike)
Hope Yeonho’s father wasn’t dead or disappeared because he want to hide the truth and save the father..