Actually no. The first to demand equal rights, quite literally too, was Lilith. First wife of Adam according to Jewish folklore. Not wanting to be completely subserviant to Adam's sexual needs she demanded to be treated as his equal (God having created her from the dust of the earth just as He did Adam, as opposed to FROM Adam.) Adam whined and bitched, and an angel of the Lord came to demand she do as Adam says. She refused, was cursed and expelled from the Garden becomming a demon. Then God made Eve from Adam's own body to be subserviant to him.
I was taught a slightly different yet very similar version.
That it was as you said, Lilith refused to be anything less than an equal to Adam (especially during sex), and when she concluded that he would not treat her as such, she went away from him and screamed out the most sacred name of God/ YHWH, and experienced an Apotheosis of sorts. She became a demon and escaped Eden using her newfound powers... through her own free Will.
When Adam learned of this, he begged God/ YHWH to return Lilith to him. God sent three Angels after her, and they found Lilith on Earth hovering over the Red Sea all badass like. They gave her a chance to return to Eden, and when she refused, they cursed her.
Since Lilith was a lost cause for Adam, God created Eve from Adam, and she became the subservient wife that Adam had always wanted.
Epic story either way you look at it.