There is a large gender gap in who chooses STEM majors, yet decades of research have failed to explain this gap in its entirety. We use extensive data on incoming college freshmen to estimate the importance of ability (both test-based and self-assessed), life goals, other self-assessed traits, high school courses, and family background in explaining the gender gap in STEM majors. Even with this detailed data, we can explain only 39% of the gender gap. A Gelbach decomposition shows that self-assessed ability (26%) and high school courses (12%) account for the bulk of the explained gap, while goals explain little and in fact controlling for goals slightly widens the gender gap. Goals are similarly uninformative of the gender gap in STEM persistence from freshman to senior year. On the other hand, goals contribute substantially to gender differences in biology and some non- STEM majors, particularly business, education, and health, but remain uninformative of the gap for the majority of STEM subjects. We conclude that while life goals are strongly related to major choice, gender-based differences in these goals are not the missing piece to the STEM gender gap puzzle.