The consequences of hybridization for biodiversity depend on the specific ecological and evolutionary context in which it occurs. Understanding patterns of gene flow among hybridizing species is crucial for determining the evolutionary trajectories of species assemblages. The recently discovered hybridization between two species of Darwin's tree finches (Camarhynchus parvulus and C. pauper) on Floreana Island, Galápagos, presents an exciting opportunity to investigate the mechanisms causing hybridization and its potential evolutionary consequences under conditions of recent habitat disturbance and the introduction of invasive pathogens. In this study, we combine morphological and genetic analysis with pairing observations to explore the extent, direction and drivers of hybridization and to test whether hybridization patterns are a result of asymmetrical pairing preference driven by females of the rarer species (C. pauper). We found asymmetrical introgression from the critically endangered, larger-bodied C. pauper to the common, smaller-bodied C. parvulus, which was associated with a lack of selection against heterospecific males by C. pauper females. Examination of pairing data showed that C. parvulus females paired assortatively, whereas C. pauper females showed no such pattern. This study shows how sex-specific drivers can determine the direction of gene flow in hybridizing species. Furthermore, our results suggest the existence of a hybrid swarm comprised of C. parvulus and hybrid birds. We discuss the influence of interspecific abundance differences and susceptibility to the invasive parasite Philornis downsi on the observed hybridization and recommend that the conservation of this iconic species group should be managed jointly rather than species-specific.