I think these romantic styles manifest differently in different cultures.

We live in a culture where men initiating romance with women is less of a one way street (women can do the initiating too), and that's a good thing I think.

That said, I don't think a man initiating with a woman is looked down on either. What is looked down on, more often, is chasing after the person has told you they aeren't interested, but that is something both men and women are discouraged to do in my experience.

The "aggressor" romance style is less about taking initiative and more about a competitive and sometimes even disdainful attitude towards one's partner. Often getting someone to take the initiative on you (compelling them to do so) is just as much an "aggressor" tactic as initiating.

Just my 2c.