Natural fliers utilize passive and active flight control strategies to cope with windy conditions. This capability makes them incredibly agile and resistant to wind gusts. Here, we study how insects achieve this, by combining Computational Fluid Dynamics (CFD) analyses of flying fruit flies with freely-flying robotic experiments. The CFD analysis shows that flying flies are partly passively stable in side-wind conditions due to their dorsal-ventral wing-beat asymmetry defined as wing-stroke dihedral. Our robotic experiments confirm that this mechanism also stabilizes free-moving flapping robots with similar asymmetric dihedral wing-beats. This shows that both animals and robots with asymmetric wing-beats are dynamically stable in sideways wind gusts. Based on these results, we developed an improved model for the aerodynamic yaw and roll torques caused by the coupling between lateral motion and the stroke dihedral. The yaw coupling passively steers an asymmetric flapping flyer into the direction of a sideways wind gust; in contrast, roll torques are only stabilizing at high air gust velocities, due to non-linear coupling effects. The combined CFD simulations, robot experiments, and stability modeling help explain why the majority of flying insects exhibit wing-beats with positive stroke dihedral and can be used to develop more stable and robust flapping-wing Micro-Air-Vehicles.