Hair Covering for Women
We learn in our parsha that part of the ordeal of the woman suspected of adultery is that the Kohen uncovers her hair (Bamidbar 5:18). The gemara infers from this that hair covering for a married woman is a Torah obligation (Ketubot 72a). However, a fascinating aggada implies that this obligation has a much older origin.
"Rav Yitzchak bar Avdimi said: Chava was cursed with ten curses". In addition to the explicit ones such as the discomfort of pregnancy and the pain of childbirth, the gemara counts that she is "wrapped up like a mourner" (Eiruvin 100b). Rashi explains that she is ashamed to go about with her hair uncovered.
If we examine the obligation for a mourner to be "wrapped up" and cover the hair (SA YD 386), we could easily connect it to another aspect of mourning: The mourner is unkempt, as cutting the hair and other grooming is forbidden (SA YD 390); covering the head may diminish the loss of dignity due to the disorderly appearance.
This relates to Chava's predicament. As a result of the sin of Adam and Chava, the romantic attraction between man and woman was admixed with an impure, bestial element. The very attractiveness of the human body now became a potential source of shame! For this reason they were ashamed to be naked after the sin, and made themselves clothes (Bereshit 3:7). For Chava this included covering her hair, for hair is part of a married woman's special attractiveness (Berakhot 24a).
However, this explanation is still incomplete. After all, both men and women began to cover themselves after the sin; why was hair covering required only of women?
Rav Kook provides an interesting explanation. The gemara in Berakhot counts three distractions which prevent a man from saying Shema with the required purity of thought: a woman's leg, her singing voice, and her exposed hair (Berakhot 24a). Rav Kook explains that these three examples represent three different aspects of feminine attraction to men: One aspect is the inherent, defining difference between the sexes. The second is a merely perceptual difference. A woman naturally has a higher and softer voice than a man, but this is not inherently related to her femininity; rather, a man perceives the difference in a woman's voice and for this reason finds it attractive.
The third kind of difference is one that is purely conventional. Unlike a woman's physique or her voice, women's hair is physically completely identical to that of men. However, since hair is uniquely amenable to being styled and adorned, women have traditionally personalized it to augment their beauty. It is for this cultural reason that women, but not men, are required to cover their hair when it constitutes an inappropriate attraction, as in the case of a married woman. (Based on Ein Ayah on Berakhot 24a)