Yup, it's just cultural inertia. You are trying to understand the situation's economics from a capitalist point of view, that the brides are "worth" something, and the investment the parents have put into their upbringing was "value" the bride's family put into the marriage, and they should be paid for that.
However, in the culture of India, the groom's family is doing the bride's family a favor by taking the bride off their hands, and undertaking caring for her for the rest of her life. Thus the bride family pays for this service. Usually the dowry is proportional to things like how undesirable the girl may be, how desirable the guy may be, the difference in social status between the parents, all favoring the guy.
Of course, the family itself thinks more along your lines -- "I have to spend money to raise her and take care of her, and then I have to spend an exorbitant amount more when she gets married as dowry," and thus end up resenting her existence from birth.
It's pretty silly, and is slowly fading away, but cultural inertia in a country as large and riveted in its ways as India is a force to be reckoned with.