Avoidance of incestuous matings is widely reported across many animal taxa, and the adaptive value of such behavior is explained through inbreeding depression. However, an old and somewhat neglected theoretical result predicts that inbred matings offer another, positive effect on the inclusive fitness of parents: an individual who mates with a relative will help that relative to spread genes identical by descent. This benefit can be substantial, if the additional mating achieved by the relative does not harm his mating success otherwise, and in the context of selfing in plants the phenomenon is well known. Here, we develop a model that derives expected values of inbreeding tolerance, that is, the magnitude of inbreeding depression that is required to make individuals avoid inbreeding, for different animal life histories and parental investment patterns. We also distinguish between simultaneous and sequential mate choice, and show that inbreeding tolerance should often be remarkably high in the latter scenario in particular, although egalitarian parental care will lead to lower tolerance. There is a mismatch between theory and data: the almost complete lack of cases where individuals prefer to mate incestuously is at odds with a large overlap between the predicted range of inbreeding tolerance and estimates of inbreeding depression found in nature. We discuss four different solutions to this enigma, and suggest that inbreeding tolerance, where it is found, should not always be attributed to a simple constraint that has prevented finding any other mate.