Gender equality doesn’t mean that everything will be the same, it means that both genders should be afforded the same rights, privileges, opportunities, and responsibilities. But there are still some physiological and biological differences that exist between the genders, so expecting that equality means that both genders will have the same behavior strikes me as a bit naive.
Now, obviously, we’re not completely equal yet, after all, it’s not all that long ago that, more or less, men were instructed by society to be the hunters and women the prey, and that men who weren’t aggressive were pansies and women who were aggressive were bitches. As society shifts more toward equality, those ideas will fade, but I still think, physiologically speaking, men will still tend to be more aggressive, if for no other reason, because men tend to have more testosterone. The main difference there, though, is that men who aren’t or women that are much less likely to be shamed for not fitting that archaic stereotype. I’m also finding that, in general, women are being more forward with approaching men. Now, I imagine part of that is maturity, as I and the women I might date get older there’s less interest in conforming to those social standards, but it does seem that dating in general is becoming more equal.
That all said, in a “truly equal” society, I still would expect that men would probably be a little more likely to be the one that approaches first, though hopefully, we’ll see more of a gravitation toward it being a mutual attraction relationship and less of a pursuer/pursued approach.