The hijab is an act of obedience to Allah, and to his messanger Muhammad (sallalahu alahe wa salam). He (subhan wa ta Allah) says: 

“ It is not for a believer, man or woman, when Allah and His Messanger have decreed a matter that they should have an option in their decision. And whoever disobeys Allah and His Messanger, has indeed strayed in a plain error.” (Quran 33:36)

Allah also says: 

“ But no by your lord, they can have no faith, untill they make you ( Muhammed) a judge in all sisputes between them, and find in themselves no resistance against your decisions, and accept them with full submission” (Quran 4:65)

Indeed, Allah ordered that women must put o­n the hijab1 He (subhanna wa ta Allah) says:

“ And tell the believing women to lower their gazes ( from looking at forbidden things) and protect their private parts ( from illegal sexual acts, etc.) and not to show off their adornment except what must (ordinarily) appear thereof, that they should draw veils over their Juyubihinna2.” (Quran 24:31)

Allah considered the dazzling display of beauty an act of ignorance: 

“ And stay in your house and do not display yourselves like that of the times of Jahiliyeeeyah (ignorance).” (Quran 33:33)

He, the most glorified, says: 

“ And when you ask the prophet’s wives for anything you want, ask them from behind a screen.” (Quran 33:53)

The above ayah does not apply o­nly to the Prophet’s wives but to all the believing women. Carefully read the folllowing saying of Allah (subhanna wa ta Allah):

“ O Prophet! Tell your wives and your daughters and the women of the believers to draw their cloaks (veils) over their bodies(when outdoors). That is most convenient that they should be known and not molested.” (Quran 33:59)

The Prophet (sallalahu alahe wa salam) said: The woman (i.e. any woman) is A’wrah,” that is she must be covered.

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Footnotes:

1This is not something cultural. It is Allahs order. Its conditions are not Arabian, Egyptian, Pakastanian, Black or White American, etc. Its conditions are specifies in the Quran and the Sunnah to provide protection and safeguarding of women. No o­ne knows about what is good for men and women more that their creator, Allah. His laws are wise as it is the case with all His actions.
2Juyubihinna: The respected scholars from As-Salaf As-Saleh (righteous predecessors) differed whether the veil cover of the body must include the hands and face or not. Today, respected scholars say that the hands and face must be covered. Other respected scholars say it is preferable for women to cover their whole bodies.
3No o­ne can ignore the molestation of women that exists in the so called “ open” societies. The question is: Why is it happening? The answer begins to shape up when people think about the purpose behind creation. Allah created us for the single purpose of worshipping Him alone. He detalied all the ways to fulfill this purpose in the last Revelation to mankind, the Quran. In it we can find how women and men can safeguard their dignity, honor, and morality. The worship of Allah is manifested in the following of his orders. Allah orders that men and women must avoid all the roads that lead to anamalistic ways of living. The hijab is o­ne of Allah’s commands. It is an honor and protection for women as well as a true freedom for her body from the hands and eyes of aggressors and molestors.