My father didn't walk me down the aisle (or the isle for that matter), nor did he "give me away" - walking down the aisle could be perfectly fine as long as the groom's father or mother did the same I guess, but "giving away" is utterly sexist and also utterly meaningless given most couples live together before marriage, not with their parents, and of course humans are no longer chattel ...
DH and I walked in together - we'd been to quite a few weddings in the run up and he strongly objected to the equally sexist tradition of the groom standing at the front looking daft and the person about to perform the ceremony making obligatory jokes about the bride not turning up
I lived with someone so didn't get married, but DD hasn't spoken to her DF since we left and when this subject came up ( we do like watching the Say Yes to the Dress programmes as DD is a fashon student) DD was adamant she will never ask her dad to walk her down the aisle as it's too sexist for her.
In fact, her preference is for walking alone, or ideally walking down with her spouse to be, whoever that is (it's all hypothetical right now).
If I met someone new and we got married, I'll be the same, as marriage should be an equal partnership and this sort of thing sets the tone.