Explainable NLP techniques primarily explain by answering "Which tokens in the input are responsible for this prediction?''. We argue that for NLP models that make predictions by comparing two input texts, it is more useful to explain by answering "What differences between the two inputs explain this prediction?''. We introduce a technique to generate contrastive highlights that explain the predictions of a semantic divergence model via phrase-alignment-guided erasure. We show that the resulting highlights match human rationales of cross-lingual semantic differences better than popular post-hoc saliency techniques and that they successfully help people detect fine-grained meaning differences in human translations and critical machine translation errors.