I believe it has much more due to the fact that men and woman already have equal rights; it's just in different areas. Giving women all the same rights as men currently have, only creates women to have more rights then men. People don't seem to see it this way but it's the truth.
Some Examples:
Married couple has a child together, they divorce, Women gets the child under just about any circumstances. It doesn't matter if the father is more fit for the job, the woman automatically has Custody to the child; assuming shes not entirely incapable of doing do. Father has to fight for custody but it's nearly impossible for a father to get full custody if the mother doesn't allow it under any circumstances. If you revert that, it's impossible for the mother to go without any custody if she doesn't agree assuming shes not abusing the child in a major way.
Men forced to pay child support or they could face prison, for women it's optional in some states of the US.
Man strikes a woman, it's automatically non-justified unless it was in self defense, but even that is limited at best.
Married couple divorces, Woman is Automatically entitled to a percentage of income/items he had made/owned. reverted; a Man is Not automatically entitled to what she had made. He must take it to court, although it can pass it's nowhere close to the chances a woman has.
Women only ventures are justified however men only ventures are illegal in most states.
Feminist organization such as the Elizabeth Fry Society push for community sentences for women. Meaning men go to jail while women that do the same crime will only receive community service in some cases.
In Sexual occurrences, if a woman claims she was drunk (Doesn't even have to be proven in some cases) and she claims to have been raped; weather she gave consent or not' it's automatically claimed as rape in court. Reverted, their has never been a successful case under the same circumstances.
This is one of the most abused false claimed crimes in the US, It's been caught quite a few times and the punishment is severe, however it's something that's nearly impossible to prove otherwise.
==Rights Men have that Woman Don't==
Can't stroll around topless in a public area.
Much more difficult to obtain combat related jobs.
In some jobs, a Female could be paid less than a male would, although this is almost nonexistent as of currently.
Of course their may be more on each side but These are the ones I know of personally (Off the top of my head) that I've seen the facts/laws for.