The search for new materials for energy -efficient electronic devices has gained unprecedented importance. Among the various classes of magnetic materials driving this search are antiferromagnets, magnetoelectrics, and systems with topological spin excitations. Cu3TeO6 is a material that belongs to all three of these classes. Combining static electric polarization and magnetic torque measurements with phenomenological simulations we demonstrate that magnetic -field -induced spin reorientation needs to be taken into account to understand the linear magnetoelectric effect in Cu3TeO6. Our calculations reveal that the magnetic field pushes the system from the nonpolar ground state to the polar magnetic structures. However, nonpolar structures only weakly differing from the obtained polar ones exist due to the weak effect that the field -induced breaking of some symmetries has on the calculated structures. Among those symmetries is the PT (1 over bar ') symmetry, preserved for Dirac points found in Cu3TeO6. Our findings establish Cu3TeO6 as a promising playground to study the interplay of spintronics-related phenomena.