The genetic systems of animals and plants are typically eumendelian. That is, an equal complement of autosomes is inherited from each of two parents, and at each locus, each parent's allele is equally likely to be expressed and equally likely to be transmitted. Genetic systems that violate any of these eumendelian symmetries are termed asymmetric and include parent-specific gene expression (PSGE), haplodiploidy, thelytoky, and related systems. Asymmetric genetic systems typically arise in lineages with close associations between kin (gregarious siblings, brooding, or viviparity). To date, different explanatory frameworks have been proposed to account for each of the different asymmetric genetic systems. Haig's kinship theory of genomic imprinting argues that PSGE arises when kinship asymmetries between interacting kin create conflicts between maternally and paternally derived alleles. Greater maternal than paternal relatedness within groups selects for more "abstemious" expression of maternally derived alleles and more "greedy" expression of paternally derived alleles. Here, I argue that this process may also underlie origins of haplodiploidy and many origins of thelytoky. The tendency for paternal alleles to be more "greedy" in maternal kin groups means that maternal-paternal conflict is not a zero-sum game: the maternal optimum will more closely correspond to the optimum for family groups and demes and for associated entities such as symbionts. Often in these circumstances, partial or complete suppression of paternal gene expression will evolve (haplodiploidy, thelytoky), or other features of the life cycle will evolve to minimize the conflict (monogamy, inbreeding). Maternally transmitted cytoplasmic elements and maternally imprinted nuclear alleles have a shared interest in minimizing agonistic interactions between female siblings and may cooperate to exclude the paternal genome. Eusociality is the most dramatic expression of the conflict-reducing effects of haplodiploidy, but its original and more widespread function may be suppression of intrafamilial cannibalism. In rare circumstances in which paternal gene products gain access to maternal physiology via a placenta, PSGE with greedy paternal gene expression can persist (e.g., in mammals).