In most bird species, dispersal distance from the natal territory to a breeding territory is greater for females than for males. Two main hypotheses have been proposed to explain sex-biased dispersal: 1) it serves as an inbreeding-avoidance mechanism or 2) it is linked to a sex difference in resource-holding potential and territory establishment. Additionally, in species where individuals delay dispersal and become subordinates in a natal territory, differences in benefits of philopatry (e.g. territory inheritance, own reproduction) may also affect sex-biased dispersal. We show that in the group-living Seychelles warbler, Acrocephalus sechellensis, females disperse further to obtain a breeding position than males do. However, we found no evidence that female-biased dispersal distance can be explained by the above-mentioned hypotheses: further dispersal does not lead to less-related partners, both sexes defend and can inherit a territory, and subordinate females are more likely to obtain some reproduction than subordinate males. Instead, we provide evidence for a little-explored hypothesis based on sex differences in dispersal costs: namely that extra-territorial forays, pursued to search for limited vacancies, are more costly for males in terms of increased mortality, although the exact mechanism for this is unclear. In line with differential dispersal costs, males foray less far than females and often wait for local dispersal opportunities, ultimately resulting in a shorter average dispersal distance. Our results may help future studies in explaining sex-biased dispersal in social and perhaps also non-social species, and we suggest some mechanisms that may explain why sex-biased dispersal differs between species.