An optical antenna forms the subwavelength bridge between free space optical radiation and localized electromagnetic energy. Its localized electromagnetic modes strongly depend on its geometry and material composition. Here, we present the design and experimental realization of a novel V-shaped all-dielectric antenna based on high-index amorphous silicon with a strong magnetic dipole resonance in the visible range. As a result, it exhibits extraordinary bidirectional scattering into diametrically opposite directions. The scattering direction is effectively controlled by the incident wavelength, rendering the antenna a passive bidirectional wavelength router. A detailed multipole decomposition analysis reveals that the excitation and abrupt phase change of an out-of-plane polarized magnetic dipole and an in-plane electric quadrupole are essential for the directivity switching. Previously, noble metals have been extensively exploited for plasmonic directional nanoantenna design. However, these inevitably suffer from high intrinsic ohmic losses and a relatively weak magnetic response to the incident light. Compared to a similar gold plasmonic nanoantenna design, we show that the silicon-based antennas demonstrate stronger magnetic scattering with minimal absorption losses. Our results indicate that all-dielectric antennas will open exciting possibilities for efficient manipulation of light-matter interactions.