Inbreeding avoidance is predicted to induce sex biases in dispersal. But which sex should disperse? In polygynous species, females pay higher costs to inbreeding and thus might be expected to disperse more, but empirical evidence consistently reveals male biases. Here, we show that theoretical expectations change drastically if females are allowed to avoid inbreeding via kin recognition. At high inbreeding loads, females should prefer immigrants over residents, thereby boosting male dispersal. At lower inbreeding loads, by contrast, inclusive fitness benefits should induce females to prefer relatives, thereby promoting male philopatry. This result points to disruptive effects of sexual selection. The inbreeding load that females are ready to accept is surprisingly high. In absence of search costs, females should prefer related partners as long as delta<r/(1+r) where r is relatedness and delta is the fecundity loss relative to an outbred mating. This amounts to fitness losses up to one-fifth for a half-sib mating and one-third for a full-sib mating, which lie in the upper range of inbreeding depression values currently reported in natural populations. The observation of active inbreeding avoidance in a polygynous species thus suggests that inbreeding depression exceeds this threshold in the species under scrutiny or that inbred matings at least partly forfeit other mating opportunities for males. Our model also shows that female choosiness should decline rapidly with search costs, stemming from, for example, reproductive delays. Species under strong time constraints on reproduction should thus be tolerant of inbreeding.