The OPs 1st paragraph is a fact. This is how women are wired. They want to be in the presence of the man who makes her "feel". Who she's really into. All women will do it. Has nothing to do with her being low self esteem. This is the natural order. Not the other way around.
Unfortunately men have been programmed to chase. Partly chivalry and partly protecting womans true nature. Its the way a modern society says things ought to be bec this false model makes woman the prize. This is a huge mistake and where the avg guy ****s up. The man's roll is to grease the wheels and set things in motion. In fact if shesnot chasing and cooperating early on she not that interested. At this point, men will act according to the BP script they've been conditioned to follow. Some will even proclaim their undying love for melady.