Spin-orbit optical phenomena pertain to the wider class of electromagnetic effects originating from the interaction of the photon spin with the spatial structure and propagation characteristics of an optical wave, medi-ated by suitable optical media. There are many emerging photonic applications of spin-orbit interactions (SOI) of light, such as control of the optical wave propagation via the spin, enhanced optical manipulation, and generation of structured optical fields. Unfortunately, current applications are based on symmetric SOI, that is, the behaviours of polarized photons with two opposite spins are opposite, leading to the limit of spin-based multiplexers. The symmetry of SOI can be broken in our proposed metasurfaces, consisting of spatially varying birefringence, which can arbitrarily and independently build SOI for two opposite spins without reduction of optical energy us-age. We obtain three kinds of dual-functional metasurfaces at visible and infrared wavelengths with high effi-ciency. Our concept of generation of asymmetric SOI for two spins, using anisotropic metasurfaces, will open new degrees of freedoms for building new types of spin-controlled multifunctional shared-aperture devices for the generation of complex structured optical fields.