Why there is difference in hemoglobin between male and female?

Menstruation. The average hemoglobin concentration in women (12-16 g/dl) is lower than the average concentration in men (14-18 g/dl) because women lose some blood during normal menstruation.
Testosterone. Although women to have a higher incidence of iron deficiency because of menstruation and pregnancies, that is actually not the reason for the lower level of hemoglobin in females. Testosterone, the male hormone, causes an increase in red blood cell production, and is responsible for the difference. In fact, testosterone derivatives are sometimes used to treat anemia.