Well, I can help you understand it from my perspective but I cannot say it would be the perspective of ALL women!
Everybody has a different idea or thought of how the male/female dynamic should go. I personally, especially at this point in my life, would not feel very "safe" being the aggressor in a R/fling/getting to know you period. I have not been around a "new" man since I have been 22 years old and what you *think* when you are 22 and what you *know* when you are 35 differ vastly.
I'm not suggesting a man be a puppet and allow the lady he is interested in to pull all the strings... not at all. Some women though (me for example) have what many might call "old fashion" ideas of how they would like a courtship/dating experience to begin.
Obviously when you meet somebody new you don't know their history and what they have experienced. How could you? I never pursued my H and he never really pursued me. He and I were VERY good friends and things sort of just happened in a very natural way. I also know that during our marriage my H was VERY lazy about being any sort of leader and I won't have that in my life again. Not everybody gets the opportunity to find a partner/R that begins with a very tight friendship (that feels safe to me) but anything else (to me) is kind of scary.
Maybe I am too skeptical but really... if a guy called me on a Sunday night to come over I would say buzz off. And if I didn't say buzz off and I did go and we "watched a movie" and I didn't hear from him again... um, no. My text would be: I'd like my ring back, when can I expect that to happen?
Like I said - maybe I am old fashion and nerdy but in the beginning I would feel much safer and at ease if the man could make some initial general gestures. If he is not cool with me needing a bit of time to let somebody new in my life AFTER a divorce, well, not much I can say about that. A man who treats a man like a lady would never have diminished value to me.