I don't think that's quite what is behind it. I think the "giving away" is what is behind virginity obsession.

The fact is that humans thrive on challenge and reward. Things we get too easily don't seem as rewarding, and therefore seem less valuable. This goes for both males and females (likely homosexual couples too) - though probably the key dynamic is hetero male-chasing-hetero female.

If she sleeps with him easily, it's less of a "score" for him. He doesn't feel that he has attained so much. That's what is meant by "easy", not that she is going to run out of sex.

The reality is that there are drawbacks to indiscriminate sex. Disease, unwanted pregnancy, the fact that many hyper-promiscuous people have low self-esteem and are using sex to assuage that. So someone not seeming at all picky, at all discriminating - male or female - loses attractiveness as a result. Not only are they not hard to get, they are actually desperate.

So in summary being more discriminate with whom you have sex with is (a) wise and (b) a more desirable trait, for BOTH genders.