Responses
I think so too. The great factor of his psychological behavior are his parents. He basically grew up in a fucked up family situation. He should see a doctor and recovery would be a tough one because this kind of psychological issue that was implanted on his mind so early already left a huge impact on himself as an individual. Sangwoo is literally stuck in his past that's why he can't move on and love someone back.
Taking aside the murders...
Sangwoo's parents completely failed him and so did society, Sangwoo wasn't born a Psychopath even if he had mental health from the start, If his parents were working together... he wouldn't of turned out like this.
Sangwoo needs help and "sharply too", who knows what he's capable of next?
I know some of you wont agree and think he should be thrown in prison or even death... But doesn't someone who's ill deserve medical treatment? Only after treatment will Sangwoo truly be able to pay for his crimes.