Most Muslim girls and women don't wear the headscarf or burqa of their own choosing. It is common practice for many Muslim schoolgirls in Europe to leave the house veiled and secretly change into casual wear on their way to school, knowing full well that if their family finds out, they would face serious consequences.
Knowing hundreds of muslims through friends and customers I've never heard of girls leaving their homes veiled and changing into casual wear, firstly you would never get away with it and secondly you can't often wear veils in school, mainly due to Health & Safety. I've heard of muslim girls leaving home dressed conservatively (ie headscarves, long sleeve tops, trousers or long skirts) then changing into lower cut sleeveless tops or skirts (or shorter skirts) if they are going to college or a party or a club etc. You'll also find that most women that wear veils in Europe do so voluntarily, I've seen women out shopping wearing veils whilst their mum or/and sometimes sister will be dressed casually with their hair flowing and make up on, this would make no sense if they were being oppressed by the males in the home, come to think of it I don't recall seeing a family where all the women were veiled, there's always a mix and some days a women will be unveiled and on another day she will have on a headscarf or veil, some days they just feel like wearing it. I think a major factor in how muslim women (and men) now dress is the war on terror, many view this as a war on islam and have isolated themselves into their own community as they feel targeted by non muslims, and the easiest way to isolate yourself is to dress differently. Over the past 5-10 years I've seen many women begin wearing veils or headscarves as well as men growing their beards and wearing traditional islamic dress and regularly attending mosques, guys who I never thought would become so religious.
Although I'm sure wearing the veil is voluntary in the majority of cases, I feel many of the women wrongly interpret what the religion asks of them, some people believe the veil is more of a cultural thing that has morphed into a religious one. In any case I'm all for the veil being banned in public places, there's health & safety and security but also in areas such as schools or workplaces I feel the veil is a barrier to effective communication and ultimately integration. Seeing someones facial expressions is key to understanding that person and getting to know them on even the basic level, if we want a harmonious integrated society we need to at least see one anothers faces, women can continue wearing their veil at home or private/family functions if they still choose to do so.