Alot of psychological research has been done to suggest that a balance of masculine and feminine "qualities", I.E/ Adrogyny, is socially more useful. Also research suggests that in all countries around the world (independent of influence) have distinct (and similar) Female and Male roles. This would suggest that there is an innate Masculine and Feminine side.
However there is a lot of debate as to what causes this difference; Biological psychologist argue for a genetic determinist view, Freud goes for an anatomical-with-bits-of-social-influence determinism.
Another interesting theory is Kohlberg's Cognitive-developmental theory and he suggests we learn gender roles through the Social Learning theory which proposes we need reinforcement and modelling of the behaviour appropriate to us, but it doesn't explain why we act in certain ways WITHOUT influence, for example children who have not been influence by gender roles still play with sex-appropriate toys like boys to guns, girls to dolls.
All in all there really are no actual FACTS about why we behave as we do, it may be one single factor, or it may be an amalgam.
From my personal experience (which isn't much I have to admit) I believe that there is something, genetic or psychic, within us that gives us a sense (nothing tangible, but just a feeling) of what we are in terms of our gender.