Given two object images, how can we explain their differences in terms of the underlying object properties? To address this question, we propose Align-Deform-Subtract (ADS) -- an interventional framework for explaining object differences. By leveraging semantic alignments in image-space as counterfactual interventions on the underlying object properties, ADS iteratively quantifies and removes differences in object properties. The result is a set of "disentangled" error measures which explain object differences in terms of the underlying properties. Experiments on real and synthetic data illustrate the efficacy of the framework.