There is no mention of Kanyadaan in the Vedas. It is mentioned in the Manu Smriti as part of many injunctions for the maintenance of the social order according to the understanding of dharma in far back days. Now Manusmriti has become dated and many of its edicts are no more followed. It is not a scripture of absolute authority and this injunction cannot be regarded as final authority. There are number of instances in the Vedic lore of great women who wrote even mantras of the Vedas but never got married, Gargi, for instance.
Besides how can one give something that never is yours except temporarily and as a Trust. It is only oneself that one has the right to give and its highest form of giving is giving oneself to the Divine. The daughter is not personal wealth or property to be given away to someone.
Affectionately,
Alok Da
