Here are some excerpts from it which also summarize what the author wants to say:
...it is been settled matter in the scriptures
that the parents do not have ownership rights over the child. The writ of the
parents does not extend enough to carry out their sale or hand them over as a
“daana”.
...The parental responsibility of the girl child
is transferred from the one performing the kanyaadaana to the prospective
husband.
So it's the responsibility that is being transferred and it is a reversible transfer. In the sense that if girl-child is divorced or widowed the responsility is transferred back to the parents. Now how many people know this? Till today I too didn't know about this and my thought was that a widow was the responsibility of the parents-in-law but that's not true. In today's age, most of the women are financially independent so maybe it's not so much of a problem but maybe a decade back it wasn't so. Parents married off their daughters and thought their responsibility was over. If she was left alone due to any reason she wasn't welcome back in her own house, the house where she spent her childhood.
I wish people would try to learn about rituals they've been following since ages. Or maybe that's why they don't.