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The polarization switching (PS) properties of mutually coupled vertical-cavity surface-emitting lasers (VCSELs) subject to variable-polarization optical feedback (VPOF) are investigated numerically. Two injection schemes, parallel-polarization optical injection (PPOI), and orthogonal-polarization optical injection (OPOI) are considered. The effects of VPOF on PS properties are focused on, and the roles of feedback strength, injection strength, and frequency detuning are also discussed. The outputs in the time domain and the polarization evolution through the representation on the Poincaré sphere are further presented to explain the dynamics during the PS process. For PPOI, both VCSELs exhibit similar PS properties, abrupt PS can be observed with the variation of polarizer angle, and are hardly affected by frequency detuning. For OPOI, both VCSELs exhibit mixed polarization for all polarizer angles when without frequency detuning. In particular, frequency detuning induced PS can also be observed for a given polarizer angle, and are affected by the leader-lagged relationship in terms of injection locking effect in mutually coupled VCSELs. These results provide an effective tool to obtain controllable PS in mutually coupled VCSELs, and give more insight into the polarization dynamics.