I don't understand how cultures where women do not have the freedom to be women and men certainly do not have the freedom to be men and live in a culture where both takes place is "Freedom."
Not long ago these cultures practiced similar customs as do Muslim cultures still practice today. My grandmother who was English always wore head covering. The Bridal veil is a throwback to the time when women war head coverings. The female settlers of the American colonies all wore headcovering and the roles were defined. More and more women complain these days about having to work and leave the kids in day care. America's whole culture and society is crumbling into a mess of dysfunctional and broken families because of their lack of freedom to be who they are.
Personally as a non muslim I like places like Italy where the men and women celebrate daily their difference in sex.
I for one as an American and non-muslim can not possibly see how what you say is happening in the west is "Freedom". It sounds and feels like demise of life to me.