I just looked in my brand new copy of the Summa Theologica (birthday present), and St Thomas says this:
“It was necessary for woman to be made, as the Scripture says, as a “helper” to man; not, indeed, as a helpmate in other works, as some say, since man can be more efficiently helped by another man in other works; but as a helper in the work of procreation.”
…and this:
"When all things were first formed, it was more suitable for the woman to be made from man that (for the female to be from the male) in other animals. First, in order thus to give the first man a certain dignity consisting in this, that as God is the principle of the whole universe, so the first man, in likeness to God, was the principle of the whole human race. Wherefore Paul says that “God made the whole human race from one” (Acts 17:26). Secondly, that man might love woman all the more, and cleave to her more closely, knowing her to be fashioned from himself. Hence it is written (Gn. 2:23,24): “She was taken out of man, wherefore a man shall leave father and mother, and shall cleave to his wife.” This was most necessary as regards the human race, in which the male and female live together for life; which is not the case with other animals. Thirdly, because, as the Philosopher says (Ethic. viii, 12), the human male and female are united, not only for generation, as with other animals, but also for the purpose of domestic life, in which each has his or her particular duty, and in which the man is the head of the woman. Wherefore it was suitable for the woman to be made out of man, as out of her principle. Fourthly, there is a sacramental reason for this. For by this is signified that the Church takes her origin from Christ. Wherefore the Apostle says (Eph. 5:32): “This is a great sacrament; but I speak in Christ and in the Church.”
…and just in case that second quote sounds too sexist (which it’s not meant to be), St Thomas also says this:
“It was right for the woman to be made from a rib of man. First, to signify the social union of man and woman, for the woman should neither “use authority over man,” and so she was not made from his head; nor was it right for her to be subject to man’s contempt as his slave, and so she was not made from his feet. Secondly, for the sacramental signification; for from the side of Christ sleeping on the Cross the Sacraments flowed—namely, blood and water—on which the Church was established.”
It’s all under Question 92, at this link:
ccel.org/ccel/aquinas/summa.toc.html
Hope that helps.
Also note 1 Corinthians 11:3.