A woman veiled could be in mourning for lost loved ones, entering a Catholic church, about to give herself in marriage, flirting ferociously with someone, or proclaiming loudly, "don't touch". There is no analog in the Attire language for men. Menswear has tended to be more direct, less subjective, and so, less prone to broad application of meaning. The veil has been the province exclusive, of women.
The veil is also an object of flirtation, even a challenge of sorts to men. Do you dare to lift my veil and face the consequences? Can you handle what you will find? Careful, this is potentially destructive. And so, the veil has a secondary layer of meanings that are connected directly to sex, sensuality, and the perceived roles of women and men together.
And gentlemen, if you dare to, this is undiscovered country. Be warned. Here there be dragons.