Sketch classification models have been extensively investigated by designing a task-driven deep neural network. Despite their successful performances, few works have attempted to explain the prediction of sketch classifiers. To explain the prediction of classifiers, an intuitive way is to visualize the activation maps via computing the gradients. However, visualization based explanations are constrained by several factors when directly applying them to interpret the sketch classifiers: (i) low-semantic visualization regions for human understanding. and (ii) neglecting of the inter-class correlations among distinct categories. To address these issues, we introduce a novel explanation method to interpret the decision of sketch classifiers with stroke-level evidences. Specifically, to achieve stroke-level semantic regions, we first develop a sketch parser that parses the sketch into strokes while preserving their geometric structures. Then, we design a counterfactual map generator to discover the stroke-level principal components for a specific category. Finally, based on the counterfactual feature maps, our model could explain the question of "why the sketch is classified as X" by providing positive and negative semantic explanation evidences. Experiments conducted on two public sketch benchmarks, Sketchy-COCO and TU-Berlin, demonstrate the effectiveness of our proposed model. Furthermore, our model could provide more discriminative and human understandable explanations compared with these existing works.