When women approach, its because the guy is displaying certain attributes. I very very rarely initiate in a way that anyone observing could say... He approached her first. If I see something that piques my interest, I just put myself in proximity and 'turn on' a set of attributes. They are compelled to approach, and in their opinion, think they initiated. Once they do, then I immediately reassert, and seize ownership. They feel desire/protected/understood, not chased. Just like HP thinks she initiated. Her H may think she did too, but that doesnt make it so.
I never gave the 'who chose who' dynamic much thought since I've never had much experience in the area, but that's really interesting.
"Happiness is a butterfly, which, when pursued, is always just beyond your grasp, but which, if you will sit down quietly, may alight upon you."