"A real woman wants man's role in society as she wants hair on her face."
I like it. I can't even bring myself to dwell for more than 5 seconds on the thought of hair on my face because it horrifies me to imagine it! And so should it be for wanting a man's place in society.
I've always been of the mind that a strong woman is a virtuous woman. I wish I had more of it. "Strength" can be a loaded term these days, as it is often confused with "masculinity." Strength is just an aspect of masculinity, not what defines it. Strength is also an aspect of feminenity.