Alterations in social cognition are hypothesized to underlie social communication challenges in autism spectrum disorder. However, the etiologic underpinnings driving this association, as well as the impact of other psychiatric conditions on the association, remain unclear. Using a co-twin control design, we examined n = 308 twins (mean age = 16.63; 46% females) with autism spectrum disorder, attention-deficit/hyperactivity disorder, affective disorders, or typical development using the Reading the Mind in the Eyes Test to operationalize social cognition ability. Clinical diagnosis of autism spectrum disorder, as well as the extent of quantitative autistic traits, as measured by parental reports using the Social Responsiveness Scale-2, predicted fewer expected responses on the Reading the Mind in the Eyes Test across the pairs. The association remained when adjusting for other diagnoses and IQ. In addition, male sex, lower age, and lower IQ predicted poorer performance on the Reading the Mind in the Eyes Test. The associations between autism and social cognition ability were lost within pairs in both the full sample and the monozygotic subsample. We conclude that the association between autism and social cognition across the sample highlights the importance of social cognition alterations in autism spectrum disorder when compared with other conditions. The attenuation of the association in the within-pair models indicate familial confounding, such as genes and shared environment, influencing both autism and social cognition.