Some selected quotes
It is an infantile superstition of the human spirit that virginity would be thought a virtue and not the barrier that separates ignorance from knowledge.
Prudishness is pretence of innocence without innocence. Women have to remain prudish as long as men are sentimental, dense, and evil enough to demand of them eternal innocence and lack of education. For innocence is the only thing which can ennoble lack of education.
— Friedrich Von Schlegel, Selected Aphorisms from the Athenaeum
It is not because it symbolises feminine virginity that integrity fascinates man; but it is his admiration for integrity that renders virginity precious.
— Simone de Beauvoir, The Second Sex
The idea that virginity represents integrity is likely to come about from the historical tendancy of men to regard women as a resource to be guarded and, if you will pardon a seriously Orwellian euphemism (but still quite accurate as quasi-agricultural metaphor), cultivated. The value that women place on their own virginity, in view of Schlegel's remarks on innocence, is essentially that this notional asset in the currency of innocence is one of the most prized things they can have, the "greatest gift a woman can give a man". Indeed, in societies that value "integrity" of this sort in a woman, to "give up" her virginity is an incredible act of trust on the woman's part, in those circumstances that she "gives" it freely (and to the extent that it is even possible that this is a free choice), because it puts her status with respect to what is these days called the virgin/whore or Madonna/whore dichotomy in a very precarious condition.
By way of contrast, a short and self-aware statement on male sexuality:
Grant me chastity and continence, but not yet.
— Saint Augustine of Hippo, Confessions
Brief remarks on medical facts and limited historical speculation
As a supplement, I'll just remark that it appears that the "folklore" about hymens — that is, the common ideas which permeate non-medical professionals — is not exactly accurate. In particular the hymen does not cover the entire vagina (which would prevent women from menstruating),
and in grown women is an elastic membrane which is not necessarily damaged in any substantial way with sexual intercourse (and may of course be damaged in other ways). See for instance the Wikipedia page on the hymen.
Of course, the idea that there could be some quite patchy medical knowledge which might inform societal values is not surprising, and we cannot expect ancient cultures to have had enough detachment (or female empowerment enough) to think about calmly about exploring such topics. The very fact that women have often not been systematically given any substantial room to direct their own lives, that women were (ahem) an object of interest for many generations of men who had substantial political power, and the very foggy notions that ancient, medieval, and even colonial western societies have had about reproduction in general (let alone the special case of the anatomy of female genitalia), went some way to permit all sorts of ungrounded ideas about "purity" and ways that "purity" might be indicated to gain currency, when it can be quite well argued that it was both (a) purely a conceptual invention except inasmuch as it was inversely correlated with the woman's experience of the world; and (b) physically accurate only to the extent that the women whose virginity was so highly prized, may not yet have actually been sexually mature.
Surely someone who is not a complete dilettante in philosophy, let alone gender studies, can write a more comprehensive answer than this. I would be happier if someone with a stronger background could make this answer quite obsolete.