What's with her dad coming out of nowhere and badmouthing her?
It's refreshing to see that Dan-I is having these thoughts, since in most isekai's the protagonist adapts to their situation relatively fast and hardly thinks about their previous life at all. I think this is about 2-3 years after the beginning of the story, however long middle school is for them. And she's been stuck playing the role of a side character all that time, watching everything happen around her. Not only that, Dan-I's also felt like an outsider, since in a past chapter she mentioned how she can't think of Ban Yeoryeong as a true friend. It's easy to see understand how she feels.
On the other hand, I initially thought Chunyoung was harsh for calling her fake, but it's accurate. If you overheard a friend saying that, the implications are bad no matter how you frame it.