Playing hard to get is a thing girls do. Trust me, I know this as a girl. It's the usual trope of pretend to not care until the end.
I would liken Sanji and Nami to Leela and Fry from Futurama who also didn't show feelings until the end. Or Ron and Kim from Kim Possible.
If I were you, I wouldn't call it playing hard to get I agree with you that you can understand your fellow man better than the opposite sex in terms of emotions, but this time I think you're wrong, it's not that important for Nami, when we look at the pleasure of caring, the person that Nami cares about the most is obviously the most special person for him, you know that, if we talk about the whole cake, Nami was ready to leave him, Luffy didn't want it.
The film Strong world is quite self-explanatory, even though it is very little stated.
I'm also very good with emotions.