Recent literature presents evidence that men are more competitively inclined than women. Since top-level careers usually require competitiveness, competitiveness differences provide an explanation for gender gaps in wages and differences in occupational choice. A natural question is whether women are born less competitive or whether they become so through the process of socialization. To pinpoint when in the socialization process the difference arises, we compare the competitiveness of children in matrilineal and patriarchal societies. We find that while there is no difference at any age in the matrilineal society, girls become less competitive around puberty in the patriarchal society.