He's not a character. He's a plot device. Can't feel bad about his bad arm because our story wouldn't have been able to do much with the MC on the bench all year. Can't feel bad about his unrequited love because we don't really know his feelings nor want him with the MC's crush. He holds no value otherwise.
I like him. In my opinion there is a reason to like him. But some people can't control their emotions so we can't hate him. I also think that since he's jealous(we've all been there) it shows how real he is and how similar he is to the readers. He also just moves the plot along so without him I don't think it would be a sign interesting.
I think Jaejin would be way more likeable if his entire character wasn't just jealousy and angst. I just...there's no reason to like him. Yeah he's got a bad wrist and an unrequited love but...what else?