Selective classification, in which models are allowed to abstain on uncertain predictions, is a natural approach to improving accuracy in settings where errors are costly but abstentions are manageable. In this paper, we find that while selective classification can improve average accuracies, it can simultaneously magnify existing accuracy disparities between various groups within a population, especially in the presence of spurious correlations. We observe this behavior consistently across five datasets from computer vision and NLP. Surprisingly, increasing the abstention rate can even decrease accuracies on some groups. To better understand when selective classification improves or worsens accuracy on a group, we study its margin distribution, which captures the model’s confidences over all predictions. For example, when the margin distribution is symmetric, we prove that whether selective classification monotonically improves or worsens accuracy is fully determined by the accuracy at full coverage (i.e., without any abstentions) and whether the distribution satisfies a property we term left-log-concavity. Our analysis also shows that selective classification tends to magnify accuracy disparities that are present at full coverage. Fortunately, we find that it uniformly improves each group when applied to distributionally-robust models that achieve similar full-coverage accuracies across groups. Altogether, our results imply selective classification should be used with care and underscore the importance of models that perform equally well across groups at full coverage.