What Tethers said (again - I'll get a fan club badge, shall I?) The opposite of modesty might be showing off in English and, actually, I have no problem with woman, man or child showing off when they are proud of themselves. We set cultural limits on acceptable amounts of showing off but, overall, self-confidence and self-worth are laudable qualities.
There is no direct translation of awrah. A poster here rudely belittled a comment of mine about honour & shame, choosing to suppose I wanted to raise the question of honour killings. I think that showed her ignorance more than mine (but then I would, heh.) In our medieval times - alongside the birth of Islam - we took the concepts of honour, shame, and modesty every bit as seriously as Islam now does. People, communities and nations were violently murdered for those ideas. In Europe, this was engendered & enforced by the Church. We've been trying to get rid of this damaging triad of notions - and their ugly sisters, pride & prejudice - for the past couple of hundred years. We're succeeding. Honour now lingers in expressions such as 'word of honour' and 'to honour a debt' but has completely lost its force as something like the Chinese 'face'. Likewise, shame lingers as a word in 'for shame' and 'shamefaced', etc, and we still feel the emotion of shame but view it as psychologically damaging. We value guilt, and seek to exorcise the burning self-loathing of shame through love & compassion. Modesty, I'm delighted to say, no longer has any physical connotations at all. It's now the cultural ceiling on showing off, that's all. Physical modesty is manacled to shame in one's body. We dislike physical shame because we see it as psychologically cancerous, therefore we cannot value physical modesty.
Once again, I'm trying to encompass a cultural megalith in one paragraph. In my perception, we dislike or mistrust the covering of muslim women because it represents a set of beliefs we've worked hard to throw off in our pursuit of individual freedoms & social equalities. So many have suffered so much for honour, shame, and modesty.
Earlier today, I spent a few hours revisiting biblical histories I haven't read for [ahem] 40 years or more, finding myself shocked anew by the terrifying control Judaism and Christianity exerted over all aspects of human life, and the grotesque punishments enacted on transgressors. (Other cultures did/do these things, too, but I'm looking at the linear progression of our monotheistic belief systems in particular.) I hope you can understand why I'm happy we no longer cut off thieves' hands, stone adulterous women or burn homosexuals. It frightens me that Islam - in the form of sharia - strives to maintain the harsh precepts of old, and to reinstate them where they had been softened. Such harsh regimes hinge upon the honour/shame principle.
Some readers will skim this post and think that [a] I'm accusing muslims of being backward; and [b] I think every observant muslim woman covers herself for fear of violence. Let me answer that [a] I accuse a majority of muslim leaders of being backward and cruel, not the religion itself or the majority of followers; [b] The fear I perceive is not a direct fear of personal violence, it's a fear of 'shame' - of loss of 'modesty'.
It would be lovely to explore the theme of honour-shame-modesty in more depth, in the specific context of Islam, but that won't work. I can only cite basics - the quran says cover your genitals, the founding hadiths give a few more rules that would be met by English workwear. After that, though, we get lost in sophistry and 900 years' worth of clerics disputing the exact meaning of each given word ... And, as long as muslem women prize 'modesty' in fear of shame, we cannot understand each other on this matter. We do not have awrah.
One thing that really, really bugs me here is that if I visit a predominantly muslim country, I cover. I do this out of respect for cultural habits and fear of what I'll suffer if I don't observe those habits. Yet muslims in this secular country seem to resent being asked to observe our cultural habits, at least in as far as dropping the dress code we find upsetting. Northern Europeans attach great importance to being able to see people's faces. So great that my gut feel is "get used to it", despite never having objected to any unusual mode of dress before in my life. I believe most non-muslem Europeans share my feeling, especially if they are bothered by gender segregation.
There's yet another very complex issue at stake, which is about multi-culturalism. France has taken a different approach because France is mono-cultural. France has government organisations devoted to keeping France French. French multi-culturalism says "Welcome, new French people!" Britain, on the other hand, aims for blended culturalism. Some other nations (I forget which) have parallel culturalism - and this is a hot topic at the moment, as we seem to have inadvertently developed parallelism while taking our governmental eye off the ball. It creates tension in the parallel communities; we just haven't got the social structures for it. We want people to blend, without having to make laws about it!
I think I'd better put my flameproof suit on.
Oh peaceful, while I'm writing Mumsnet's longest post 
'It perpetuates male power over society, and women who wrap up are complicit.' - This for me is the most dangerous idea expressed here as it is victim blaming
How can it be victim-blaming if the women are not victims?