Accurate phylogenies are crucial for understanding evolutionary processes, especially species diversification. It is commonly assumed that "good" species are sufficiently isolated genetically that gene genealogies represent accurate phylogenies. However, it is increasingly clear that good species may continue to exchange genetic material through hybridization (introgression). Many studies of closely related species reveal introgression of some genes without others, often with more rapid introgression of maternally inherited chloroplast or mitochondrial DNA (cpDNA, mtDNA). We seek a general explanation for this biased introgression using simple models of common reproductive isolating barriers (RIBs). We compare empirically informed models of prezygotic isolation (for pre- and postinsemination mechanisms of both female choice and male competition) with postzygotic isolation and demonstrate that rate of introgression depends critically upon type of RIB and mode of genetic inheritance (maternal versus biparental versus paternal). Our frequency-dependent prezygotic RIBs allow much more rapid introgression of biparentally and maternally inherited genes than do commonly modeled postzygotic RIBs (especially maternally inherited DNA). After considering the specific predictions in the context of empirical observations, we conclude that our model of prezygotie RIBs is a general explanation for biased introgression of maternally inherited genomic components. These findings suggest that we should use extreme caution when interpreting single gene genealogies as species phylogenies, especially for cpDNA and mtDNA.