Haplodiploidy has evolved repeatedly among invertebrates, and appears to be associated with inbreeding. Evolutionary biologists have long debated the possible benefits for females in diplodiploid species to produce haploid sons-beginning their population's transition to haplodiploidy-and whether inbreeding promotes or inhibits this transition. However, little attention has been given to what makes a haploid individual male rather than female, and whether the mechanism of sex determination may modulate the costs and benefits of male haploidy. We remedy this by performing a theoretical analysis of the origin and invasion of male haploidy across the full range of sex-determination mechanisms and sib-mating rates. We find that male haploidy is facilitated by three different mechanisms of sex determination-all involving male heterogamety-and impeded by the others. We also find that inbreeding does not pose an obvious evolutionary barrier, on account of a previously neglected sex-ratio effect whereby the production of haploid sons leads to an abundance of granddaughters that is advantageous in the context of inbreeding. We find empirical support for these predictions in a survey of sex determination and inbreeding across haplodiploids and their sister taxa.