This is an old and a difficult question. I guess thousands of men hit their heads on stone to find a rational answer to this. Jacques Lacan, a well known french philosopher, says the following story regarding this.
"Let's imagine a person X is sitting alone in a restaurant and a couple enters from the door. X notices the couple. Whom from the couple (man or woman) will X quickly stare at? If X is a man, of course he will stare at the woman. There's no question about it. However, if X is a woman, upon which one do you think her eyes will quickly land on? The man? Not really. She too will check out the woman. But why? Admittedly, and understandably, the woman's object of desire is the man. However, that itself does not drive her gaze. What she is really interested on is the woman whose object of desire is the same man. Who is the woman who wants this guy? Why does she want him? This is what drives a woman's gaze."
Confusing enough? However I think one cannot blame the author because of the inexplicable nature of the subject. I read this in an article written by Lacan some time back and repeated it in my words. In my experience I can say that Lacan was particularly correct here.
Inspired by many experiences, I created the following story to express my opinion on this. It is described in the form of an experiment.
Go to a guy and offer him a pencil. He might accept it with gratitude or refuse it giving a reason. Pretty simple. Now approach a girl and offer the pencil. Most probably she will refuse it with some reason. Now you have to say this. "Fine, that other girl loves pencils. I'll give it to her then". At this point I can predict the girl's response precisely. "No, No; Don't give it to her. Give it to me."
The story might sound silly, but I suggest you (especially if you are a guy) to put it in parallel to your life experiences and check.
Although I'm not smart enough to come up with a satisfactory answer to the original question, I think this post can be ended with the following useful conclusion.
"A woman wants something only if she knows that another woman also wants it"