If a woman expects a man to pay on a date (which many do), it means she sees herself as being better than him in some way, that's why she expects him to pay for her. Only a narcissist would do this. You can see this alot more clearly if you switch the roles so that its the man expecting a woman to pay for him.

Both men and women can be narcissistic, but society tends to encourage narcisism in women. The fact that many women are preoccupied with their looks, for example is another sign of narcissism. The whole makeup and fashion industry is based on female narcissism.

I think you have to be at least a little bit narcissistic to spend a lot of time looking in the mirror and applying powder on your face, which artificially enhances your appearance.