Dubai actually isn't a country -- it's the biggest city in the United Arab Emirates. I decided to go over to a big Freedom House article on women's rights in lots of different North African / Middle Eastern countries and see what the situation in the UAE with regard to women's rights is. Sentences dealing with the UAE specifically:
In the UAE, the law requires a woman to surrender her UAE citizenship if she marries a man who is not a citizen of a Gulf state."Free and rich" indeed. They've also got a big set of rankings of countries in the region with regard to women's rights. Even among the 16 countries in that benighted region, the UAE scores in the bottom 3 on "Nondiscrimination and Access to Justice", gets mediocre scores on "Autonomy, Security, and Freedom of the Person," does slightly better on "Economic Rights and Equal Opportunity," is again in the bottom three on "Political Rights and Civic Voice" due to denial of women's suffrage, and does pretty badly on "Social and Cultural Rights" as well.
Independent women's groups advocating for women's legal equality are not permitted to openly operate in the UAE or Saudi Arabia.
As Matt says, this is what happens when your conception of freedom is "lower taxes for rich people" rather than anything involving, say, women being able to vote. Which gives you an idea where the Independent Women's Forum's priorities are.