depends on what you're talking about you don't need a man for.
to my knowledge, i don't know one woman regardless of race who hasn't been told, "make sure you can take care of yourself so you don't have to depend on a man." and so the girl goes out trying to be self-sufficient financially. which is good. because every woman should be able to take care of herself. our moms weren't lying.
it's just that what people need isn't just limited to material means. and there are other things we can get from men besides financial security. and i think a lot of times when women say they don't need a man, they are either ignoring or not mindful of the other stuff that you can get from being in a good relationship with a man... maybe that's 'cause there are some real f'd up relationships out there and maybe it's easier for some women to see the drawbacks than the benefits...
anyway i think that attitude does affect our relationships with men - i could be wrong here, but seems like to me everyone wants to feel needed, including men. shoot, especially men. if you treat somebody like you don't need them, and their upbringing has taught them that part of what defines them is their ability to take care of others, well damn. you just blew some isht up. if a woman makes 100x what her man makes, there's still some things he can do for her that she can't do for herself... and she needs to recognize that.
this isn't to say single women are incomplete without men. they are a complete woman. but just like with food and seasoning, the presence of a good man in a woman's life can enhance the quality of her life. and unfortunately, i don't think we hear this lesson as often as we hear "you can do bad by yourself," and the good message gets drowned out by the cautionary tale.