Coccoids (scale insects) exhibit a wide variety of chromosomal systems. In many species, paternal chromosomes are eliminated from the male germline such that all of a male's sperm transmit an identical set of maternal chromosomes. In such species, an offspring's sex is determined by whether or not paternal chromosomes are inactivated in the egg's cytoplasm after fertilization. This paper presents a model of the evolution of paternal genome loss in coccoids from an ancestral system of XX-XO sex determination. The model is based on Hamilton's (1967) theory that different genetic elements within the genome have different unbeatable sex ratios. In this model (1) meiotic drive by the X chromosome in XO males causes female-biased sex ratios; (2) the maternal set of autosomes in males evolves effective sex linkage to exploit X-drive; and (3) genes expressed in mothers are selected to convert some of their XX daughters into sons. A similar model may explain the evolution of haplodiploidy.