The hijab isn't only the veil and isn't about seclusion; it is modest clothing and behavior in general for men and women, adults and children. Of course both the general and specific meanings came defined through time. The first of them was the specific which was limited only to Muhammad wives. Who's reasoning for came from their home being the Mosque itself and hence lacking the privacy of wives of other households wore the hijab to compensate. The verse of the Quran that establish the specific tradition of hijab is as follow: "Believers, do not enter the Prophet's house…unless asked (ex. for daily prayers). And if you are invited…do not linger. And when you ask something from the Prophet's wives, do so from behind a hijab. This will assure the purity of your hearts as well as theirs" (33:53).
Even than the specific tradition of hijab wasn't new to the Arabs of which Islam in general made it initial rise among. The tradition dated back to earlier Arab contacts with women of the upper classes of Iran and Syria who like Muhammad wives, homes were not as private as the average woman. Furthermore the term for donning the veil and becoming Muhammad's wife are one in the same: 'darabat al-hijab.' The hijab in the specific sense was classically a luxury and hence a sign of power not oppression. Additionally those that force the specific hijab on women fail to recognize that by forcing modesty they make it into a fetish which in turn mutes the whole purpose of a hijab in the first place. While those that would force woman to rid their selves of it engage in sexual assault.
Muslimphobics in the West that complain about the hijab must not wear any bottoms as they gawk at every member of the opposite sex like dogs in heat! That or they simply know as little about Islam as they do their own culture. Even in the West staring is considered rude and to go about having anatomy unique to gender exposed illegal on not just religious but common secular grounds. The Quran when making general prescription of hijab simply tells Muslims of both sexes not to ogle at members of the opposite sex when met and to cover their anatomy unique to their gender. There would be no need for such rules if seclusion - weather by shelter, partition in Mosque, or clothing such as burqa and niqab, etc. - was the mode of norm in Islam. The rules of hijab in the Quran were created in a society where traditionally men and women both went out in public. Besides how can one remember their brothers and sisters in faith if they never see them in the first place?
In the life of Muhammad men and women, young and old, prince and piper all stood and prostrated their selves shoulder to shoulder in prayer. The mosque during prayer would have been one scenario Muslims practice hijab in the forms already discussed. A less specific but not as general purpose of the hijab as simply being modest clothing and behavior could have come from the notion of covering one head during prayer to remind oneself of God's position above. Many Jews, Christians, and Muslims to this day practice such still. Many women who don't wear the headscarf hijab (and men that don't wear other head garb) normally for modesty don the hijab for this pious purpose. Some go further with this more pious than modest purpose: as Muslims are to think of Allah in all they do many will wear head garb at all times as physical remembrance of Allah position above them at all times.

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My Islamic Primer for You - Some Answers for My Friends
Non-FictionMy Islamic primer from my religious studies course on Islam. Had to write a 5 to 7 pages primer on Islam for someone not familiar with Islam in double space 12 point Times News Roman font.