Anisotropic magnetoresistance (AMR), originating from spin-orbit coupling (SOC), is the sensitivity of the electrical resistance in magnetic systems to the direction of spin magnetization. Although this phenomenon has been experimentally reported for several nanoscale junctions, a clear understanding of the physical mechanism behind it is still elusive. Here we discuss a novel concept based on orbital symmetry considerations to attain a significant AMR of up to 95% for a broad class of $pi$-type molecular spin-valves. It is illustrated at the benzene-dithiolate molecule connected between two monoatomic nickel electrodes. We find that SOC opens, via spin-flip events at the ferromagnet-molecule interface, a new conduction channel, which is fully blocked by symmetry without SOC. Importantly, the interplay between main and new transport channels turns out to depend strongly on the magnetization direction in the nickel electrodes due to the tilting of molecular orbital. Moreover, due to multi-band quantum interference, appearing at the band edge of nickel electrodes, a transmission drop is observed just above the Fermi energy. Altogether, these effects lead to a significant AMR around the Fermi level, which even changes a sign. Our theoretical understanding, corroborated in terms of textit{ab initio} calculations and simplified analytical models, reveals the general principles for an efficient realization of AMR in molecule-based spintronic devices.
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