Or why the daughter hasn't told her dad that's she's a lesbian?
je gyung has been pretty consistently characterized as someone concerned with others and how her actions affect them. it's neither an unsympathetic situation nor a strange/out-of-character stance for her to take, at the very least compared to the other more contrived plot beats.
we get a more explicit look at her thought process at the end of ch21: she's afraid of how coming out could affect her dad, who she believes to have enough interpersonal burdens wrt stability as-is. between being widowed (to a late wife whose world he "always worked hard to keep getting invited"), having an emotionally estranged extended family, and a daughter living abroad, it's understandable she has reservations about coming out and possibly "taking" one of the last close relationships he has left in his life.
granted, some of that last part is definitely projection and more a personal fear of change on je gyung's part. she knows how one's opinion can do a 180 on even family or a lover for reasons out of their control. she's afraid her being a lesbian could cause her dad to resent her, paralleling how her grandfather treated her dad following the economic crash, and even more personally, her ex-girlfriend leaving her after falling in love with a man.
and even if her dad has shown interest in her love life, and even further that he doesn't find same-sex relationships strange, this isn't the same as being explicitly told that you'll be loved and treated the same after coming out. it's unfortunately not uncommon for people to "tolerate" homosexuality in people outside their circles only to be uncomfortable with or outright reject lesbian/gay friends or family members.