Irony in The Rights of Woman

Barbauld's The Rights of Woman is a response to Mary Wollstonecraft's A Vindication of the Rights of Woman. For the majority of the poem it seems like she's completely agreeing with Wollstonecraft's train of thought that women should stand up for equal treatment and deserve the same opportunities. This would make sense because she grew up in a place where she was given a good education. It also seems like Barbauld got really lucky because her father taught at a school for boys, and she probably shouldn't have gotten such a good education, but because her father worked there, she was allowed a lot of the same opportunities. This story is very similar to that of Huda Shaarawi, leader of the Egyptian feminist movement in the early twentieth century. A really outspoken woman, who was very close to her brother, and upon seeing the unequal treatment, demanded that she receive the same opportunities, particularly in education. Coming to the end of Barbauld's poem, I realized that she had stopped agreeing with Wollstonecraft. Barbauld essentially tells women to forget what she said at the beginning and stop being so aggressive because "Subduing and subdued, thou soon shalt find/Thy coldness soften, and thy pride give way" (27-8). Here, she describes the reaction a woman will have to finding a good relationship with a man. She goes on to talk about how "separate rights are lost in mutual love" (32). Barbauld is telling her female audience that a good relationship leads to apathy regarding equal rights and opportunities for women because a good relationship makes all of that not matter. At the beginning of this poem, I was wondering why this poem hadn't received any serious backlash, but upon reaching the end, I realized why. I just assumed that because she had been so fortunate with the education she received, she would want to try and send the message that education and equal treatment is important, but instead she falls right into the patriarchy of the time and tells women that they don't really need to stand up for their rights, instead, she says a happy marriage is the true source of happiness.