Not exactly. They’re not signing away their virginity. Their dad does not own the virginity.

They’re promising to preserve their virginity for a future husband. They’re promising their dad they will do this, presumably for themselves. However, since they’re usually too young when they do this it’s clear they don’t have a full understanding of what it entails or what it even means. From the little girl’s perspective it’s just a promise she makes so she can wear a pretty dress, have a special day with dad, and it makes him happy.

That means that once they get to be old enough to understand what sex is and to start to desire it, most of them break that promise (usually by technicalities) with little angst because it was a coerced promise and not legally binding anyway.

The interesting question is what do the dads get out of this? False honor and a fake prize that was meant to be a gift to someone else in exchange for wealth back in the day, the biblical days that is.

That’s not any less creepy and maybe I’m picking at semantics but virginity is a state of being, not an identity and you cannot sign over, cede control of, or barter a state of being.