Is it the case that women almost always make the first move?

I got into the same argument today I always do with my male friends:

It is my strong belief that women always make the first move. Sometimes it is subtle eye flirting, sometimes something more blatant.

Is the idea that men initiate a fallacy? I am willing to accept once a woman generates interest men often do most of the chasing.

I am also curious as to any insight members of the GLBT community might feel they can provide about the first initial encounters in their relationships.