It always struck me as odd that Lee-Yun (Weed) never caught on to how terrible he was at singing, despite numerous people flat out telling him he's terrible. Even if he's tone deaf, he should at least be able to recognize how bad he is by other's reactions. However, when you look at Lee-Hyun's past and his subconscious habit of not trusting others except for his family, then it kinda begins to make sense why he doesn't believe them when they say he's terrible. Also, aside from his sister and grandmother, Lee-Hyun had no friends and since those two probably never told him he was bad (probably to avoid hurting his feelings), it stuck to him that his singing was good.
It's been shown numerous times that Weed will exploit, manipulate, and scam almost everyone so that he can make more money. After finding out that he's spent most of his life struggling to work to take care of his family, it makes you really wonder just what kind of individuals Lee-Hyun met growing up that could twist his mind to such an extent. The only thing keeping him going is the desire to protect his family, so god only knows how much more fucked up his mind would be if he ever lost them like his parents.