I don't think the author mentioned a specific reason but I guess cuz the family has that trivial idea of relationships and close minded about it. U would think that dojin is doing just fine but he looks like he doesn't feel comfortable with them himself also dowon compared to his brother has much more of a sense of freedom than the other so the type of ppl has it hard with close minded ppl like dowon's fam.
You will have to go all the way back to the beginning of this comic for that. If I remember correctly.... The parents used to fight a lot, and the father left them. It was the mother who raised both Dowon and Dojin by herself. I vaguely remember the impression of the boys father being abusive and a shitty husband....
I don't remember much involving the family but why exactly does Dowon not get along with his family except the mom?