Light beam hits the mirror perpendicularly and returns to the source (left picture). The same system in horizontal motion (right picture) is skewed due to length contraction so that both beam and mirror are at higher angle. Because the beam returns to source in the system's rest frame, it must do that in any other frame. So the beam returns the same path that is drawn with solid red line, although it might be expected that the light is reflected to direction pointed by thin dotted red line. Contrastingly, let's have a system that has the shape of right picture in its own rest frame. In this case, the light reflects so that it follows the thin dotted line. I find this distinction strange, because light reflection should depend only on the geometry. The geometry is exactly the same in both cases.