Aristotle is quite against all of it, as you will discover. But it may not be clear from what you read here why Plato was in favor of it. There's an interesting piece in the Virginia Quarterly Review on different historic ways of thinking about whether there is a female conscience -- not in the sense of whether women have a conscience, but about whether it is the same for men and women. (Spoiler: the author's position is that it is just exactly the same.)
As she points out, Plato made room for women in the highest classes (the guardians). However, there was a price for admission:
When a guardian woman gave birth, her child was taken at once to a special section of the city. There, minders cared for the young. When a child needed to nurse, he or she was handed randomly to a lactating female. Why all these wrenchings? In addition to the hope that breeding between superior males and females would continue to perpetuate an aristocracy of the best and the brightest, it was held that private homes, sexual attachments, and dedication to personal aims would undermine a citizen’s allegiance to the city. Plato cried: “Have we any greater evil for a city than what splits it and makes it many instead of one? Or a greater good than what binds it together?”It turns out there is a greater evil, and a greater good as well.
By the way, I don't think that Dr. Elshtain is quite right about Plato's position, which is more emphatically in favor of women in the guardian class than she seems to suggest. Plato is so persuasive on the point that the Islamic philosopher Averroes, in his commentary on Plato's Republic -- I notice Dr. Elshtain doesn't mention it -- takes a much more radically egalitarian position on women than a contemporary American would think to expect from an Islamic law judge. He seems to bring a large part of that philosophical position into his sha'riah intepretations as well.
I was also surprised by her insistence that the idea of women's equality is a product of Christianity, as I'm far more familiar with people complaining just the opposite about it. But she has an argument here, too, and on reflection it's a good one. The Gospel of Luke in particular seems to show a Jesus relating to women in a way that suggests that the divine position is to hold them in respect and honor.