Deep learning methods, although effective in their assigned tasks, are mostly black-boxes with respect to their inner workings. For image classification with CNNs, there exists a variety of visual explanation methods that highlight parts of input images that were relevant for the classification result. But in many domains visual highlighting may not be expressive enough when the classification relies on complex relations within visual concepts. This paper presents an approach to enrich visual explanations with verbal local explanations, emphasizing important relational information. The proposed SymMetric algorithm combines metric learning and inductive logic programming (ILP). Labels given by a human for a small subset of important image parts are first generalized to a neighborhood of similar images using a learned distance metric. The information about labels and their spatial relations is then used to build background knowledge for ILP and ultimately to learn a first-order theory that locally explains the black-box with respect to the given image. The approach is evaluated with the Dogs vs. Cats data set demonstrating the generalization ability of metric learning and with Picasso Faces to illustrate recognition of spatial meaningful constellations of sub-concepts and creation of an expressive explanation.