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It is not a gender thing. It is equally applicable if a man wants to veil himself.
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Hiding the body in a total all enveloping burqa is one extreme, and walking nude in public is the other extreme. You will see that the public dress code tries to find a middle ground between these two extremes. But the extremists (Burqa-ists, and nudists) both would oppose that and we understand why.
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Hearing lectures on secularism and free speech from Islamists is a ironic at the very least.