Parental conflicts can lead to antagonistic coevolution of the sexes and of parental genomes. Within a population, the resulting antagonistic effects should balance, but crosses between populations can reveal conflict. Parental conflict is less intense in self-pollinating plants than in outcrossers because outcrossing plants are pollinated by multiple pollen donors unrelated to the seed parent, while a self-pollinating plant is primarily pollinated by one individual (itself). Therefore, in crosses between plants with differing mating systems, outcrossing parents are expected to "overpower" selfing parents. We call this the weak inbreeder/strong outbreeder (WISO) hypothesis. Prezygotically, such overpowering can alter pollination success, and we argue that our hypothesis explains a common pattern of unilateral incompatibility, in which pollen from self-incompatible populations fertilizes ovules of self-compatible individuals but the reciprocal cross fails. A postzygotic manifestation of overpowering is aberrant seed development due to parent-of-origin effects such as genomic imprinting. We evaluate evidence for the WISO hypothesis by reviewing published accounts of crosses between plants of different mating systems. Many, but not all, of such reports support our hypothesis. Since parental conflicts can perturb fertilization and development, such conflicts may strengthen reproductive barriers between populations, contributing to speciation.