Huh

Well, the reason she can't go back home on her own is because she's a noble's daughter, a noble woman, and a daughter of nobility couldn't move around without a chaperone (at least) and guards to "protect her virtue", since she always depended on people's opinion that there were enough grounds to think "she was still a virgin", since only as an alleged virgin would she be able to get a husband of equal status, which was the only way a woman from the nobility could secure her own future livelihood (since they wouldn't know how to otherwise, as they weren't raised being taught how to do everyday work, etc)

If the white haired guy was the one who took her, people would start gossiping they were secret lovers, and/or that the real reason she had gone MIA on her father was that she had eloped with a man... both of which would have destroyed her chances of a "good marriage" (as in, one with a man of "equal" or "higher" noble status).