The speaker of "The Rights of Woman" is almost certainly a woman. And boy, does she have an axe to grind.
She spends most of the poem trying to convince women to stand up for themselves and to take over the world. She's trying to inspire the troops, and she gives one heck of a pep talk. She calls on her fellow ladies to put on their metaphorical armor and to pick up their metaphorical weapons and to lead a revolution.
But by the end of the poem, she pulls back—she says that women might get lonely at the top and have a hard time maintaining their power after kicking out all the guys. She says that this question of asserting equal rights is pointless in a relationship in which the man and the woman love each other equally anyway. So is the speaker being sarcastic in the early part of the poem? Or does she actually change her mind partway through? It's hard to tell. One thing about this speaker is sure: she's a tough nut to crack.