Part of the history is that, according to Biblical scripture, there used to be a price paid for the daughter of a gentleman. The idea was that the woman would no longer be a working member of the father's family. (!) The price was measured in other property, paid to the father.
Some men prefer to ask their future in-laws for their blessing rather than to ask for permission. Blessing implicitly acknowledges everybody’s autonomy, and permission evokes ideas of the prospective fiancée as property and of a bride price payable in goats.