So I guess I'm not alone here. I always cringe very subtly and invisibly when that word "man" is applied to me. I'm male by all evidence, but I've never really embraced masculinity by any more than a sort of experimentation. When I was growing up, I spent an inordinate amount of time and energy studying other boys and men to determine how I was supposed to act and, presumably, eventually feel. As I once wrote in a song: Once it all seemed so simple/pretty good at playing the role. I'm a pretty accomplished actor and mimic; that's how I learned to cope. Never really grew into the role and found a place that was comfortable; it was always like playing a role or carrying a mask around.
In fact, I believe that the effort of studying and play-acting severely limited my career development and general "success" in life. So many here write about demanding, traditionally alpha careers from which CD is a time-out escape, of being happy "normal" husbands and fathers, of being nuts for sports or cars or whatever. I am very handy and can fix the car or remodel a house, but those are just learned skills that are certainly not gender-exclusive.
I had one faltering, unhappy marriage relatively young (22) and then was alone for 25 years because I knew there was something different about me and didn't feel it was fair to enter into a permanent partnership with an unsuspecting woman who would likely have cultural expectations that I couldn't meet. I was never motivated to father children. I enjoy the role of grandpa to my wonderful second wife's grandchildren, but it's just another role; I've seen it done by others and learned that gig too. It has its moments, which do make me wonder what if, but...
But, there's always a melancholic backbeat of gender ambiguity and discomfort. I don't really feel like one or the other, and I don't see that ever changing.
One weird thing is that I may have learned the roles so well that no one suspects. I had a brief relationship fifteen years ago with a woman who mentioned several times that she liked decidedly masculine men, and I asked her why she liked me, then. She was taken aback and wondered why I would respond that way. We lived in different cities, and at the time, I was also going out as my feminine persona pretty regularly out of town. So, to me, I felt androgynous at best but came across to her as comfortably masculine.
The line you have identified between "man" and "male" is profoundly significant to me. The latter is a physical, biological fact; the former is a cultural construct that doesn't interest or fulfill me.