Considering that in Western society, the man is traditionally the pursuer and the woman the pursued

A more accurate way of putting that is that the man is the first to break plausible deniability. If you also take into account non-verbal, indirect signals (where if the recipient isn't interested they can just pretend to not notice and nothing bad happens), most of the times the very first move is the woman's, both according to this report about Britain and in my experience in both Italy and Ireland: I can't say I can recall ever getting a positive reaction from approaching a woman who wasn't already smiling at me. Now, a guy who has good social skills but poor introspection may only approach women who are smiling at them but not be consciously aware that he's preselecting women that way; likewise, a socially savvy but not introspectively savvy woman may not be consciously aware that she's smiling at the guy she likes; as a result, it feels to them like it's the man who's initiating the interaction, which I guess is the main cause of that confusion.