God made Adam and Eve to work together side by side, but some say that since Adam named the animals and he named Eve, that by virtue of naming them, he gained the right to rule over animals and women.  But we women are not in the category of the animals; we—unlike animals, are made in the image of God! (Genesis 1:26.27) The Hebrew verb translated as “called” or sometimes as “name” means to “call out” as in calling upon the name of God but when Adam called out, “Ishaah” (or woman), it was more like exclaiming,” Wowie kazowie!” than naming.* He wasn’t ruling, he was rejoicing! (Genesis 2:23) Later, after they sinned, Adam prophesied that Eve would be the mother of all the living—same word, in this case he called out what the future would hold. (Genesis 3:20)

*From a class in Hebrew