Is independence a turn-off?

I know a chic on another site who is always saying she is 'too much to take' for a guy. She is a single mother, has a stable job, strong opinions, she isn't afraid to try and fix things around her home with out help. These are all things that I would think are attributes, however men find them to be turn-offs. Why? Why is it that men aren't interested in independent women? This friend of mine and myself are very similar in the aforementioned ways. I don't think I had ever thought about my independence and responsibility being turn-offs until she mentioned it. Now it just confuses me.
In becoming a parent, I have changed in many ways. I have grown up and become responsible and stable and independent. I can unclog my own sinks, paint my house, change out my radiator hose, balance a checkbook, shop on a budget. I have learned to do everything myself because there was no one to ask for help. I learned very quickly that I actually like doing things myself. If I have to move my washer and dryer in and hook them up myself, I am glad to because I can. If my tire blows out, I can change it myself. I can assemble my entertainment center, I own tools and know how to use them.
I have become very comfortable in myself. I know who I am. I know what I do and do not believe as well as what I will and will not tolerate. Is that bad? Are men looking for women who don't know who they are yet? Are they looking for needy chics? Do they need to be depended on in order to be secure in a relationship?
I would love to hear some comments on this.
~Kate