I am also very independent. I am proud that I can take care of myself. At 33, I don't NEED a man around, but I would LIKE to have a man around. However, it's always been important to me to be able to take care of myself and not have to rely on someone. I know too many women who can't (or haven't tried to) take care of themselves, so they've been in and out of relationships since they left high school.
I find that men are attracted to my independence....well, they think they are. They've had needy women and are initially attracted to me because I can take care of myself. But then I think they change their minds. Men seem to be programmed to be needed, so I've definitely tried to show the new man in my life that I do need him.
The other reason I'm single? Partly because I am afraid to end up like so many other people as a single mom sharing custody with her ex. I work with children everyday, and I am so tired of seeing them pushed and pulled in all directions between parents. :-(