Evolutionary biologists mostly assume that polygyny increases sexual dimorphism in size because, under polygyny, larger males monopolize mating opportunities and pass on their 'large male' genes to their sons. Available data on parent-child correlations in height among humans (Homo sapiens) do not support the crucial assumption that height is transmitted along sex lines. This paper instead suggests that human sexual dimorphism in size emerged, not because men got taller, but because women got shorter by undergoing early menarche in response to polygyny. It further speculates that, rather than genetically transmitted, the sexual dimorphism may emerge anew in each generation in response to the degree of polygyny in society. The analysis of comparative data supports the prediction that polygyny reduces women's height, but has no effect on men's, and is consistent with the speculation that the origin of human sexual dimorphism in size may be cultural, not genetic.