Biological materials are largely anisotropic regarding their microstructure and mechanical properties. The contrasting properties in different axis creates extraordinary materials with intricate characteristics such as wood, where the alignment of the microstructure enhances stiffness on the longitudinal section rather than the radial, and bone, with not only elastic modulus but also fracture toughness highly dependent on the orientation of osteons. There is extensive research regarding the anisotropic mechanical characteristics of materials such as elastic modulus and hardness. However, our study aims to bring wear resistance correlation to microstructure to the spotlight. "Wear" is a complicated phenomenon that emerges from contact stresses and involves damage by localized yielding and cracking thus it is not an intrinsic property but rather influenced by the two in-contact bodies. Considering stresses during blunt contact, the index of H³/E², where H is hardness and E is the elastic modulus of the studied material, has been shown to well correlate with its capacity to resist wear damages. Nevertheless, this index is only valid for frictionless contacts and homogeneous isotropic materials. As biological and bioinspired materials are mostly heterogeneous and anisotropic, there is a great need to understand their behavior under wear loads. In this study, we analyzed the wear resistance of the wandering spider (Cupiennius salei) claws. The structure is made of a cuticular material, a biocomposite where chitin fibrils are embedded by a proteinaceous matrix. The cuticle is formed by three regions, epi-, exo- and endocuticle, each with contrasting orientations of the chitin fibrils. For example, in the exocuticle, the chitin fibers are oriented parallel to the claw longitudinal section. Nanowear tests, where a 1 μm conospherical tip abrades a longitudinal section of the claw, showed contrasting results depending on the tip movement direction, despite a local constant H³/E² index. This highlights the inconsistency in the wear index for anisotropic materials and indicates the need for understanding wear on heterogeneous structures.