An enormous list of Muslim women testified they had no choice. To give you some names: Chahdortt Djavann, Ayaan Hirsi Ali, Samira Bellil, Fadéla Amara, ...
Worldwide most Muslim women are forced to wear a goody-goody veil. In some countries by law, in other countries it's a man who's deciding they have to wear it. And if they do not, the women are beaten or locked up at home.
Sometimes they have a choice, but when they opt not for the veil, they are excluded from the family or local community. What a choice.
And if the above is not applicable, how much choice do you have when they
I've a Muslim friend, she has 2 children, aged 9 and 11 years. She's wearing a veil, her children only when they go the Muslim school in the weekend.
She said her oldest child may choose next year if she want to wear the veil permanently or not. But does the child have a real choice? Not, not all. That child is currently learning in the Muslim school that being unveiled is close to disgust.