Inclusive fitness theory, also known as kin selection theory, is the most general expansion of Darwin's natural selection theory. It is supported by female-biased investment by workers in the social Hymenoptera where relatedness to sisters is higher than to brothers because of haplodiploidy. However, a strong test of the theory has proven difficult in diploid social insects because they lack such relatedness asymmetry. Here we show that kin selection can result in sex ratio bias in eusocial diploids. Our model predicts that allocation will be biased towards the sex that contributes more of its genes to the next generation when sex-asymmetric inbreeding occurs. The prediction matches well with the empirical sex allocation of Reticulitermes termites where the colony king can be replaced by a queen's son. Our findings open broad new avenues to test inclusive fitness theory beyond the well-studied eusocial Hymenoptera.