In other words, there does seem to be a relationship between SG size  and social perception, but it is not a simple male-female difference.  Rather, the SG appears to reflect a person’s “femininity” better than  one’s biological sex: women who are relatively less feminine show a  correspondingly smaller SG compared to women who are more feminine, and  ditto for men.
This finding—that brain structure correlates as well or better with  psychological “gender” than with simple biological “sex”—is crucial to  keep in mind when considering any comparisons of male and female brains.  Yes, men and women are psychologically different and yes,  neuroscientists are uncovering many differences in brain anatomy and  physiology which seem to explain our behavioral differences. But just  because a difference is biological doesn’t mean it is “hard-wired.”  Individuals’ gender traits—their preference for masculine or feminine  clothes, careers, hobbies and interpersonal styles—are inevitably shaped  more by rearing and experience than is their biological sex. Likewise,  their brains, which are ultimately producing all this masculine or  feminine behavior, must be molded—at least to some degree—by the sum of  their experiences as a boy or girl.
And so, any time scientists report a difference between male and  female brains, especially in adults, it begs the question, “Nature or  nurture?” Is women’s larger SG the cause of their social sensitivity, or  the consequence of living some 30 years in a group that practices  greater empathetic responding? Wood and colleagues are among the few  neuroscientists to analyze male-female brain differences for their  relationship to gender type, as opposed to strict biological sex. Their  findings do not prove that social learning is the cause of male-female  differences in the brain, but they do challenge the idea that such brain  differences are a simple product of the Y chromosome.
http://www.scientificamerican.com/article/girl-brain-boy-brain/