Yes, injured Woman! rise, assert thy right!Woman! too long degraded, scorned, opprest; (1-2)
Women are finally breaking free, and the speaker is cheering them on. Starting the poem with that "YES!" makes it sound like the speaker is cheering for something that's already happening, even if it's really something that she's trying to encourage in the future. She's giving one heck of a pep talk to these "injured" ladies.
Like sacred mysteries, which withheld from fame,Shunning discussion, are revered the most. (15-16)
The speaker claims that women's rights are like these sacred mysteries that no one is allowed to see or even to discuss, so women's rights will get more respect. That seems kind of weird, especially because one of the complaints that some feminists in the 18th and 19th century had about how they got treated was that men treated them like they were sacred angels and kept them confined in the house. The men said that women would get more respect if they didn't go gallivanting off around the city. So the men said that these women, by "shunning discussion," would be more "revered."
But the feminists said that they didn't really need that kind of worship. They didn't want to be confined inside of the house, and they'd rather have a chance to gallivant, thank you very much. So here, Barbauld seems to be using what was usually an argument against women's rights and using it as an argument for women's rights. Very strange. Is Barbauld actually saying that women's rights shouldn't be discussed at all? Or is she being ironic? It's hard to say…
Thou mayst command, but never canst be free. (20)
Here, the speaker says that women can command men only, but they can't be too free, or too careless, in how they deal with men. But that word "free" has a double meaning here. The speaker is suggesting that women are basically sentencing themselves to a life sentence without parole by taking up rule over men. They can never, ever let their guard down, or they'll lose control. So much for the freedom they were fighting for.