Women start fewer businesses than men. The start-up rate among women in Germany falls short of males' start-up rate by one third. We scrutinize this gender gap using individual-level data from the KfW Start-up Monitor, a large-scale population survey on start-up activity in Germany. As a unique feature, the data combine socio-demographic characteristics, entrepreneurship-related attitudes, and general personality traits of both business starters and non-starters. Estimating binary choice models and employing decomposition techniques, we find that gender differences in socio-demographics alone would even be in favor of higher start-up rates among women, while the distribution of personality traits is less favorable for business start-ups among women and explains about one third of the entire gender difference. Most substantially, men opt for a start-up more often even given identical human capital and related endowments. Qualificational policies targeted towards higher educational attainments of potential entrepreneurs do thus not suffice to increase the number of female business starters.