"The Rights of Women" sounds exactly as it should—like a battle cry for women's rights. You can imagine bugles and drums and the sound of marching (female) soldiers as you listen to this poem.
The alliteration of "Soften the sullen, and clear the cloudy brow" in line 22, for example, adds to the musicality of this poem. Same deal with the internal rhyme between "man" and "command" in lines 19-20. All of those internal repetitions make the poem sound more like a song. In fact, you could imagine it as a kind of rallying song, like a national anthem or a patriotic hymn, like "The Star-Spangled Banner," "The Battle Hymn of the Republic," "God Save the Queen," or "La Marseillaise."
Notice how at least some of the lyrics to all of those songs have to do with war and with crushing enemies? Maybe that's why "The Rights of Women" sounds so much like a female national anthem. At least at the beginning, it's all about going to war and crushing women's enemies. So head over to the "Best of the Web" section and listen to this poem read out loud—maybe you'll find yourself feeling inspired and ready to go to war for women's rights.