Unsupervised stereo matching has received a lot of attention since it enables the learning of disparity estimation without ground-truth data. However, most of the unsupervised stereo matching algorithms assume that the left and right images have consistent visual properties, i.e., symmetric, and easily fail when the stereo images are asymmetric. In this paper, we present a novel spatially-adaptive self-similarity (SASS) for unsupervised asymmetric stereo matching. It extends the concept of self-similarity and generates deep features that are robust to the asymmetries. The sampling patterns to calculate self-similarities are adaptively generated throughout the image regions to effectively encode diverse patterns. In order to learn the effective sampling patterns, we design a contrastive similarity loss with positive and negative weights. Consequently, SASS is further encouraged to encode asymmetry-agnostic features, while maintaining the distinctiveness for stereo correspondence. We present extensive experimental results including ablation studies and comparisons with different methods, demonstrating effectiveness of the proposed method under resolution and noise asymmetries.