Rarely do women get to vote in Muslim societies either... and that's geerally in the most westernized of Islamic states.
In the Early 20th century, the Arab world was beginning to discuss western ideas... then WWI came, and the Ottoman Empire sided with Austria-Hungary. After being soundly defeated, the victors carved up the Middle East with either no regard for culture-groups or with a deliberate desire to divide and conquer, and installed puppet governments.
There was great unrest, though only one country managed to actually overthrow its government. That was Turkey, lead by a former officer in the Ottoman empire. When he took over, he removed that Caliphate, gave women the right to vote, changed the country to Roman writing, put in Western dress codes, and secularized the government. He strongly believed that the country needed to learn from the west to move foward.
The rest of the Arab world saw this as pandering to the bad-guys, and were likely only more enraged by the fact that it worked. In the 1920s, in Egypt, a group formed called the "Muslim Brotherhood". This can be divided into basically two sub-groups. Those who wanted to retrun to an idealized version of "the grand old days" by preaching, and those who felt that Islam was on the brink of collapse and had to be rescued by violent overthrow, the removal of all things western, and the reinstatement of religious law.
Here's where some stuff starts to really sound familiar. Citing women working as destroying the family (don't the Christians cite this over homosexuality?), and likely wanting to feel in control in a society where they had little control, the Brotherhood (mostly affluent, educated muslims) asserted that the Muslims had strayed from the true religion and therefore been abandoned by God, and that they needed a strict, anti-western, anti-woman, Islamic state to regain some imaginary golden age and protect Islam from Satan.
Wow, that sounds familiar. The Taliban is saying it. Al Quida is saying it. Much of the Muslim world is performing some form of it.
It's all about the politics. It seems that the modern Muslim support for the opression of women has many of the same causes and the Southern US support for slavery. Most whites in the souh did not have slaves, but they felt disinfranchised and out of control to the detriment of the black people in America. The Brotherhood, and their ideological descendants have done something similar with women.
Not that there isn't a basis in the Quran for women as property. It was a progressive book in it's time, but it was progressing from a Jewesh position where women are property. Islam made them somewhat less property and gave them more rights. It was a step in the right direction at the time (muh as granting protections to slaves was a step in the right direction), but is archaic by modern standards.