I haven't read all the comments here, and I'm not Muslim, so I come from a non-authoritative position in this thread. But women's issues strike a chord with me, and I have a few thoughts if you'll tolerate them.
First, the most common reason I've heard for women covering their heads is for modesty's sake, so I'll focus on this. Modesty is only related to sexuality. There is no other reason to dress "modestly", and this of course isn't unique to Islam. I have a rich and varied background in fundamentalist Christianity where the fetishism of virginity equals that of the porn industry. (I wrote a paper for school on how Christian sects and the porn biz both fetishize virginity.) The message we love to constantly send our girls is that their worth is in their sexuality. Not their talents. Not who they are.
This is not what we teach boys, though. We rather shrug our shoulders and tell them to be careful. The problems is that these boys are having sex with these girls. And the girls suffer the social stigma, but the boys don't. You can't teach one part of society one thing and another a different thing and expect good results. Islam seems to be similar to my outsider view.
Next, whether one religion or culture values a segment of society is connected to autonomy, self-determination, and freedom. One way social class is easily identified is when a segment of society is required to do something that another segment isn't. There is a difference between a woman freely choosing to cover her head or not, and her being required to at the cost of legal or social consequences.
Last, social class is often not apparent to the class on top. I read somewhere that the highest echelons of society don't need to take into consideration the concerns of the subordinated classes, don't need empathy, don't need to understand the needs of the lower classes. But to survive, the subordinated classes need to understand the top class. And the subordinated classes may not move with freedom without severe consequences like the ruling class may. I'll translate this into what I see of some cultures. Men may have affairs, vote, go to school, dress any way they see fit, work, drive cars, etc. Women are restricted by law, social custom, and religious prohibition to varying degrees in different countries in many of those areas.
That's it for now. Got children to feed, papers to write, and global domination plans to finish.