If I remember right, there's a part where jungwoo said that he didn't realized because he'd only focus on himself and I know it's ridiculous but the mind is something really powerful you know? There are things that you won't be able to see even if they are in front of you or are obvious if you don't want to see it. I think that scene more than "seeing" or not the marks, it's a metaphorical way for jungwoo to realize that people around him are struggling, that he may be having a hard time but he's not the only one.
They had sex several times and didn't notice each other's cut marks on wrist? :/