The lack of women in leadership across higher education has been problematised in the literature. Often, contemporary discourses promote "fixing the women" as a solution. Consequently, interventions aimed at helping women break through "the glass ceiling" abound. We argue that the gendered power relations at play in universities cause entrenched inequalities to remain in place, regardless of measures implemented for and by women. This article reports on a study of the impact of COVID-19 on 2029 women academics in South Africa. We examine how academic women's roles as nurturers at home are extended to their roles as carers at work, and how these impact their prospects for career progression. The article further shows how expectations placed on women academics as carers contribute to gendered dimensions of inequality that are detrimental to both their own well-being and careers. Finally, we call on higher education institutions to "fix themselves", rather than "the women", if they want to dismantle gender inequalities.