There were Jews in the city of Medina where Prophet Mohammed ruled.
The women of Jews wore the hijab, then some of the Jews started to embarrass the Muslim women with some impolite words, so the aya 33: 59 was revealed, which means:
{33: 59. O prophet, tell your wives and daughters, and the women of the believers, that they should cast their outer cloaks a over their persons.
That is most convenient b, in order that they should not be recognized and so not annoyed c. And God is Most Forgiving d, Most Merciful e.}
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a Such cloak is to cover the body of the woman, and with which Jewish women used to wrap themselves, as do Iranian women also wrap themselves with, and which they call ‘Chadre’.
It means: they put the cloak on their faces and wrap their bodies with it, lest they should be known by the Jews, dwelling in the city of Medina, and the hypocrites: know that they are Muslims, and so may speak against them with improper words among themselves and backbite them
b More close to the veiling, honor, righteousness and better outcome.
c It means: If the woman is wrapped with her cloak, none of Jews and hypocrites may recognize her, and so she will be safe of their mockery and hurt.
d Concerning their past act of forsaking the ‘Hijab’ [: the veil and cloak.]
e To them when He commanded them with the ‘Hijab’ [: the veil and cloak], in order that they may not be recognized.
Moreover, Christianity originally is more strict in this hijab, see what the nun wear.
An Italian minister once said: "How can I prevent that which Virgin Mary wore!?"
So why is all this noise; this is to the advantage of the religion of the Islam which will prevail in the end.