Q. Aside from the fact that a Yarmulke is part of men’s clothing, why are men alone obligated to cover their heads, to be aware of Who is above them? Why don’t women have such an obligation?
A. We assume that the question is being asked by an unmarried woman, since otherwise she must cover anyway her hair.
I heard in the name of Horav Brodsky Zt’l that the reason is that women’s necessary care and obligation of dressing with modesty and discretion and properly covering their bodies, represents already their respect to the presence of Hashem, so no head covering is necessary.
Horav Shlomo Miller’s Shlit’a opinion is that men require a head covering since by their given nature they posses a stronger urge and sexual desire than women do, so they require greater tools of awareness to feel constantly Hashem’s presence.
Rabbi A. Bartfeld as revised by Horav Dovid Pam, Horav Aharon Miller and Horav Chanoch Ehrentreu Shlit’a