Actually I used to. I like the many responses that many others have wisely given to you: that being a man has to do with chivalry, responsibility, maturity, self-awareness, compassionate dealings with other people... Also I like the ones that say that being a man is about the XY chromosomes, the right “plumbing” and our own ideas about what a man is.
But I'll confess that when I felt that way these ideas didn't do much for me: I’ll still felt less of a man. I was trapped between not wanting to further hurt my pride (Of course I am a real man!) and my lackful feelings (But I lack this and that that real men have!) In my case, I got over it because of two seemingly unrelated things in my life: I learned to be in contact with my feelings and I decided I would go after those things that would “make me a real man”, perhaps even "straight" if that was possible (as per many books some well meaning, but not very knowleagable in such matters people provided me with)
It was a big goal, so big and important to me that I gave up on my pride (one big feat in my case I might add!) to accept I was after something I felt I didn’t have and, eventually, achieve it. Instead of denying the lackful feelings and just try to make them go away or just toughing them trough, I acknowledged them and saw them as indicators of perceived not yet met expectations of mine. I found a pretext (the being a real man goal, useful and valuable but a pretext nonetheless) not to deny my feelings about the subject anymore. Also I had a pretty nice idea of how my goal felt (more clearly because of the contrast with my current feelings) which gave me a motivation not to dwell too much in my feelings of being-less-than. If I did feel less of a man, I’d let it be, perhaps I even would gain a certain self-insight, but after that, I’d let the feeling go in peace.
After a while, it became clear those perceived not yet met expectations were either legitimate places where I could improve myself or just perceptions that came out of others’ expectations. But whenever I was honest about where I could improve or where I was compromising to others’ expectations, not one time did I found out it had anything to do with being gay. I’ll be honest and say that sometimes it made it easy to see other straight men struggling with the same issues I had: I just happened to have a very prominent and socially awkward (gay!) characteristic in whose neck I could easily hang the “fault” and then emotionally beat myself to a pulp for being that way.
Subtlety and slowly my goal changed from “being a real man” to being the man I wanted to be (the man part of it being real became a given). So yes, I’ve chosen to make mine many of the characteristics other posters mentioned as part of the (MY) definition of manhood but also I am unashamed of my little quirks that somehow stretch or stick out of the manliness’ social expectations box (here in Mexico, being gay for instance!). I guess in a nutshell what happened to me is: I accepted how I felt, I decided not to deny it, I was very mindful of how I wanted to feel, I found ways to try to get to that “feeling place” (in my case with goals I knew were good for me and were attainable, but I guess someone more mindful than me would be able to do it without the “achievement” or “testing myself” factors) and then discovered... (And I said this stressing how I didn’t see it that way until I had made the journey) I was already there. In my case, of course it was important to me, of course it was not a very little part of my identity, of course I needed to deal with it before moving on, of course it became a big brick in the foundation of my identity, but yes, after a while, that brick is important for the whole building, but not the building itself and while I can see the case for that one brick’s absence not causing the whole to collapse, I feel better having that space filled and it was, and is, a worthwhile journey.