Tool‐using primates often show sex differences in both the frequency and efficiency of tool use. In species with sex‐biased dispersal, such within‐group variation likely shapes patterns of cultural transmission of tool‐use traditions between groups. On the Panamanian islands of Jicarón and Coiba, a population of white‐faced capuchins (Cebus capucinus imitator)—some of which engage in habitual stone tool use—provide an opportunity to test hypotheses about why such sex‐biases arise. On Jicarón, we have only observed males engaging in stone tool use, whereas on Coiba, both sexes are known to use tools. Using 5 years of camera trap data, we provide evidence that this variation likely reflects a sex difference in tool use rather than a sampling artifact, and then test hypotheses about the factors driving this pattern. Differences in physical ability or risk‐aversion, and competition over access to anvils do not account for the sex‐differences in tool‐use we observe. Our data show that adult females are physically capable of stone tool use: adult females on Coiba and juveniles on Jicarón smaller than adult females regularly engage in tool use. Females also have ample opportunity to use tools: the sexes are equally terrestrial, and competition over anvils is low. Finally, females rarely scrounge on left‐over food items either during or after tool‐using events, suggesting they are not being provisioned by males. Although it remains unclear why adult white‐faced capuchin females on Jicarón do not use stone‐tools, our results illustrate that such sex biases in socially learned behaviors can arise even in the absence of obvious physical, environmental, and social constraints. This suggests that a much more nuanced understanding of the differences in social structure, diet, and dispersal patterns are needed to explain why sex‐biases in tool use arise in some populations but not in others.