The two kinds of sex chromosomes in the heterogametic parent are transmitted to offspring with different sexes, causing opposite-sex siblings to be completely unrelated for genes located on these chromosomes. Just as the nest-parasitic cuckoo chick is selected to harm its unrelated nest-mates in order to garner more shared resources, sibling competition causes the sex chromosomes to be selected to harm siblings that do not carry them. Here we quantify and contrast this selection on the X and Y, or Z and W, sex chromosomes. We also develop a hypothesis for how this selection can contribute to the decay of the non-recombining sex chromosome.