The canonical beating of the human sperm flagellum is postulated to be symmetric. This is despite the reported asymmetries inherent to the flagellar axonemal structure, from distribution and activation of molecular motors to, even, the localisation of regulatory ion channels. This raises a fundamental question: how symmetric beating is possible within such intrinsically asymmetric flagellar complex? Here, we employ high-speed 3D imaging with mathematical analysis capable of resolving the flagellar movement in 4D (3D+time). This reveals that the human sperm beating is both anisotropic and asymmetric, and composed by a superposition of two transversal waves: an asymmetric travelling wave and a symmetric standing wave. This novel anisotropic travelling-pulsation mechanism induces sperm rolling self-organisation and causes a flagellar kinematic illusion, so that the beat appears to be symmetric if observed with 2D microscopy. The 3D beating anisotropy thus regularises the intrinsic flagellar asymmetry to achieve symmetric side-to-side movement and straight-line swimming.