Like...Psychopathic people don't have a smaller brain. Not even the parts of brain that process emotions. They just don't work and react properly. Though I don't think Sangwoo is a psychopath, but more of a sociopath. There's no point in trying to figure out why his mother was behaving the way she was since it's not like sangwoo could have been heeled anyways after her ravages. He was so severly mentally scarred, he could never be treated. On top of that, since he's a sociopath, the treatment would only treach him how to manipulate others better (putting aside that it would have been pointless anyways, since he would have never gotten out of the prison). Tho I personally suspect that he would just not react to anything.
*This is only my opinion and how I view the manga, and oh god its devastating like Zankoku Na Kami Ga Shihai Suru
This manga shows how criminals are nurtured by the society, sangwoo’s mom made him to have twisted love and belief (manipulate emotion). Sangwoo in his twisted way trying to love Bum because he is divided between loving and knowing his mom is sick, therefore cant trust anyone (seeking emotional stability). They are not mentally stable, and this is the problem with the lack of understanding of imbalance chemical brain in head with the criminals in Asia I believe (I dont want to generalise this, please someone can correct the fact). Theres suggestion that brain also develops smaller in psyhopatic person causing the emotion doesnt progress properly.
Even with Sangwoo forever in life prison, he really need a good psychiatrist to coax him to open up his experience, to heal, to get a better treatment and sentences (for Bum too). God knows how the mom can be like that, could be genetical or/both environmentally similar to sangwoo turned her like that. Man I wish theres sometimes better education m way to raise kids. Its a sad sad world guys