The retention of the concept of virginity as a prize to be won or a gift to be given on a wedding night is barbaric and extremely offensive.
First, it implies that people, especially women (since this standard is more heavily applied to them by repressive societies), are either property or have property-like aspects. It is an artifact from a time when women were considered to be literally the property of their fathers, and became the property of their husbands at marriage. A human being is not an object to be bought, sold or traded. Therefore, any fabricated immaterial aspects of that person (e.g. the psycho-spiritual concept of virginity) are also not rightly exchangeable*.
Second, it implies that your sexuality should rightly be controlled by others; that your sexuality is not yours to express as you see fit, but is the dominion of others and only valid with their assent.
You cannot give another person your virginity, because there is nothing to take. You have not lost something the first time you have sex, because there was nothing there to lose. Sex is a dynamic experience, not a static state of being. The fact that you have not had sex cannot be cut off of you and put into a jar.
A virgin is not "pure" because sex is not a matter of subjective morality. Sex is part of being human. It is something humans do. It is not, itself, right or wrong. Like anything else, of course, it can be used to hurt, or oppress, or dominate or exploit, but those qualities are not inherent to sex. To claim that a person who has had sex is somehow "dirtier" or "less good" than a person who has not is viciously repugnant.
There is no denying that a first sexual experience is powerful. There is no denying that it can have a large psychological impact. As such, it should occur under circumstances of your choosing. You want it to be with someone you love? Fine, great. You want it to be quick and anonymous? Whatever floats your boat. But dispense with this notion that virginity can be given, or taken, or traded. It cheapens us all.
*Note: this is not intended to imply that the act of sex cannot or should not be bought or sold. The purchase of a sex act does not necessarily imply ownership of the person providing the service, or their sexuality. Or it shouldn't, anyway.
In reply to Jaez' writeup:
I apologize for not being sufficiently clear. The second half of my writeup was intended to express my belief that one's virginity or lack thereof has absolutely nothing to do with whether or not one is an "honorable" or "virtuous" person. My personal definitions of those superlatives do not recognize bald notions of chastity as an inherently "good" thing. Belief systems that do elevate virginity and chastity to such heights are usually the same ones that are exploitative, oppressive and dogmatically moralistic.