Sex-determination genes are among the most fluid features of the genome in many groups of animals. In some taxa the master sex-determining gene moves frequently between chromosomes, whereas in other taxa different genes have been recruited to determine the sex of the zygotes. There is a well developed theory for the origin of stable and highly dimorphic sex chromosomes seen in groups such as the eutherian mammals. In contrast, the evolutionary lability of genetic sex determination in other groups remains largely unexplained. In this theoretical study, we show that an autosomal gene under sexually antagonistic selection can cause the spread of a new sex-determining gene linked to it. The mechanism can account for the origin of new sex-determining loci, the transposition of an ancestral sex-determining gene to an autosome, and the maintenance of multiple sex-determining factors in species that lack heteromorphic sex chromosomes.