I've been dating this girl for about 3 weeks (5 dates or so). I've tried to keep text messaging to a minimum (i.e. mostly logistics to set up the next date). Last date, however, she told me she doesn't like our post-date lack of communication, and would love to hear more from me in-between dates. I told her she can reach out for me too (she did that for a while, but recently not so much), and that I'm too busy for that anyway, but she insists it's the "man's role" to initiate contact, at least in the first few months.

So on the one hand, I don't want to follow the rules like a robot (using the phone for logistics only) - especially when she explicitly told me she doesn't like that, but on the other hand, I don't want to initiate contact 100% of the time because it might lower her attraction for me. Any advice?