"Why did freedom for women expand at some times and places in the ancient world but..."?

Well, it's an interesting question, but I don't really know what the answer is. The position of women as regards legal rights, education, means of making a living etc, has always fluctuated somewhat in different societies and different periods of history, and it is not always easy to understand why.

Ideas about what is appropriate for women change, sometimes quite suddenly. Like for instance when Napoleon came to power in France, all the legal rights that had been granted to women, like being able to obtain divorces from abusive spouses, pensions for war-widows etc, were done away with. Napoleon disapproved fiercely of women having any freedom at all.

And sometimes rights could be granted to women out of expediency. for instance in ancient Rome all women were officialy under the authroity of the male head of the family, whoever he might be, but in order to encourage women to have more children, the emperor Augustus made a law that a free woman who had three children, or a freedwoman who had four, was exempt from male guardianship. He hoped to increase the birthrate by doing this.