Male and female homosexuality have substantial prevalence in humans. Pedigree and twin studies indicate that homosexuality has substantial heritability in both sexes, yet concordance between identical twins is low and molecular studies have failed to find associated DNA makers. This paradoxical pattern calls for an explanation. We use published data on fetal androgen signaling and gene regulation via nongenetic changes in DNA packaging (epigenetics) to develop a new model for homosexuality. It is well established that fetal androgen signaling strongly influences sexual development. We show that an unappreciated feature of this process is reduced androgen sensitivity in XX fetuses and enhanced sensitivity in XY fetuses, and that this difference is most feasibly mused by numerous sex-specific epigenetic modifications ("epi-marks") originating in embryonic stem cells. These epi-marks buffer XX fetuses from masculinization due to excess fetal androgen exposure and similarly buffer XY fetuses from androgen underexposure. Extant data indicates that individual epi-marks influence some but not other sexually dimorphic traits, vary in strength across individuals, and are produced during ontogeny and erased between generations. Those that escape erasure will steer development of the sexual phenotypes they influence in a gonad-discordant direction in opposite sex offspring, mosaically feminizing XY offspring and masculinizing XX offspring. Such sex-specific epi-marks are sexually antagonistic (SA-epi-marks) because they canalize sexual development in the parent that produced them, but contribute to gonad-trait discordances in opposite-sex offspring when unerased. In this model, homosexuality occurs when stronger-than-average SA-epi-marks (influencing sexual preference) from an opposite-sex parent escape erasure and are then paired with a weaker-than-average de novo sex-specific epi-marks produced in opposite-sex offspring. Our model predicts that homosexuality is part of a wider phenomenon in which recently evolved androgen-influenced traits commonly display gonad-trait discordances at substantial frequency, and that the molecular feature underlying most homosexuality is not DNA polymorphism(s), but epi-marks that evolved to canalize sexual dimorphic development that sometimes carryover across generations and contribute to gonad-trait discordances in opposite-sex descendants.