The title "The Rights of Women" seems simple enough, right? But given when the poem was written, the title is clearly a shout-out to Mary Wollstonecraft, who published A Vindication of the Rights of Woman in January of 1792. One of Mary Wollstonecraft's main arguments was that women should have equal access to education so that they could become equal partners in marriages, if not active participants in the English workforce. Wollstonecraft complained that it was society and social training that forced women to act all docile and weak, but that given a chance and some good schooling, women could accomplish as much as men could. Rock on, Wollstonecraft, we say.
This is an attitude you'd think that Anna Barbauld could get behind—after all, she managed to persuade her own father to give her the kind of education usually reserved for boys. But her poem, "The Rights of Women," seems to take Wollstonecraft's argument and make it sound more extreme than it really was. Wollstonecraft never argued that women should actually rule over men; she just wanted equal access to education (among other things).
Some critics of Wollstonecraft certainly did try to shut her down by saying, "Next you'll want to arm women and make them stage a revolution against men, like the revolution in America or in France!" It could be that Barbauld's poem was meant to be ironic—that it's meant to show how ridiculous that criticism of Wollstonecraft really was. Then again, it could be that Barbauld really was trying to criticize Wollstonecraft directly. It's hard to say for certain, since we can't ask Barbauld what she intended—that is, unless you guys are skilled in the art of time travel. All we can do is read the poem as carefully as possible and think about it for ourselves.