I find it pretty strange that Euripides wrote this play about a woman protagonist. Women had practically no rights back in these days, and most men went along with and did not question this. As the textbook points out, Euripides's contemporaries were not very fond of his work. I think it may quite possibly be because he takes a sort of feministic approach in his writings (at least in Madea). Euripides is not simply writing about a typical day in the life of a Greek woman. Rather, he addresses social matters from a woman's perspective. One quote that stands out to me in these first few pages is, "What they say of us is that we have a peaceful time living at home, while they do the fighting in war. How wrong they are! I would much rather stand three times in front of battle than bear one child" (621). Of course, the "they" refers to Greek men. Euripides is distancing himself from who he actually is (a man), and showing the audience a side of society they don't typically get to see. Norton sums up this idea nicely when he writes, "The myth is used [by Euripides] for new purposes, to shock the members of the audience, attack their deepest prejudices, and shake them out of their complacent pride in the superiority of Greek masculinity" (615). I don't assume that many writers typically write about matters they do not believe in. So, Euripides probably actually really did support women's rights. It's interesting to consider whether or not there were many more people, besides women, who also were supporters of equal rights in Ancient Greek times.
As a side note, he even sort of "disses" men and writes, "It is the thoughts of men that are deceitful, their pledges that are loose" (625). This is coming from the mouth of a woman in the play (as is my quote above), which may sometimes throw us off. But, when you remember who it is that is actually writing the play, the answer introduces a whole new perspective in our reading.