I think for her, its about the fact that she's known for being a female mage, so they might connect the dots that she's aage living with them when they're well known for hating mages (plus they've talked plenty about how much they hate lies and the likes) and for the parents, I believe it might be because they felt as if they had constantly been forcing her to conform to a more masculine way, and/or the fact that she never felt safe enough with them that she could tell them she was female. I haven't read any raws or novel (if there is one) but that's my guess

What’s this about again, why so fixated that she’s a girl than a boy? Or is she his real daughter? I’m mixing sht up