The occurrence of polygyny (multiple queens sharing a nest) and polyandry (multiple mating by queens) in social insects, has long puzzled evolutionary biologists. If genetic relatedness is the main incentive for cooperation, how do we explain the occurrence of mechanisms that reduce the degree of relatedness among colony members? A much discussed hypothesis has it that genetically diverse colonies are more resistant to parasitism and disease than homogenous colonies, because genetic diversity reduces the spread of a disease within a colony. However, and this is not often realized, the parasite hypothesis implies as well that genetically heterogeneous colonies are likely to have a larger suite of parasites or diseases that are capable of infecting them. From this it follows that even if the cost per infection is reduced, this may not be sufficient to offset the increased rate of acquiring infections. Our analysis suggests that conditions that favour genetic heterogeneity as an anti-parasite strategy in social insects can be quite narrow.