Introducing asymmetry in capacitively coupled plasmas (CCPs) is a common strategy for achieving independent control of ion mean energy and flux. Our 1d3v particle-in-cell/Monte Carlo collision (PIC/MCC) simulations reveal that a uniform magnetic field within a specific range can induce spatial asymmetry in low-pressure CCPs, even under perfectly symmetric conditions. This asymmetry, characterized by a shift in the plasma density distribution and significant differences in electron kinetics between the two sides of the plasma, leads to strong ionization and most electron losses on the low-density side, while the high-density side experiences weak ionization and minimal electron losses. The underlying mechanism triggering this spontaneous asymmetry is the differential influence of the magnetic field on low-energy (local) and high-energy (relatively nonlocal) electrons. Under conditions of low pressure and an appropriate magnetic field, this disparity in electron kinetic behavior leads to a spontaneous amplification of the asymmetry induced by random fluctuations until a steady state is reached, culminating in an spontaneous asymmetric effect.