I believe uncledark has touched on something here when he mentioned "non-assertive." For some reason, I think there is an burden on the man to be assertive to a degree. I know I am now making claims with nothing but anecdotal evidence, however, in my experience, men are usually the ones trying to "pick up" or "come on to" women. There have, of course, been many notable exceptions, but that happens when I try to describe an ill-defined phenomenon with broad stereotypes on the internet,

Maybe it goes down to schema: we learn things from watching, and we learn how to date by watching movies and television, and mostly from people older than ourselves. Regardless, we seem to fall into the trap that a guy is expected to make the first move, and women are supposed to attract a man.

I'm not making value judgements on this, just saying that it happens. If I'm right, it's probably a problem because the situation encourages aggressiveness and sexism (the schema is very close to competing for a resource, and I can safely say that human beings should not be treated as such) and screws with our ability to relate to each other. The "nice guy" is often a person who is too respectful of space and boundaries to take a chance at an unwanted advance... he's not going to attempt to assert his presence on a female. Which get's into a whole other slew of moral dilemnas, because if that's the schema going on in the Nice Guy's head, he's kind of bought into the "women as resources" concept.