Textured hydrophobic surfaces that repel liquid droplets unidirectionally are found in nature such as butterfly wings and ryegrass leaves and are also essential in technological processes such as self-cleaning and antiicing. In many occasions, surface textures are oriented to direct rebounding droplets. Surface macrostructures (>100 mu m) have often been explored to induce directional rebound. However, the influence of impact speed and detailed surface geometry on rebound is vaguely understood, particularly for small microstructures. Here, we study, using a high-speed camera, droplet impact on surfaces with inclined micropillars. We observed directional rebound at high impact speeds on surfaces with dense arrays of pillars. We attribute this asymmetry to the difference in wetting behavior of the structure sidewalls, causing slower retraction of the contact line in the direction against the inclination compared to with the inclination. The experimental observations are complemented with numerical simulations to elucidate the detailed movement of the drops over the pillars. These insights improve our understanding of droplet impact on hydrophobic microstructures and may be useful for designing structured surfaces for controlling droplet mobility.