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Current definitions of aromaticity are purely phenomenological and relate symmetry, reactive stability and the occurrence of molecular diamagnetic response currents. The antithetical concept of antiaromaticity provides a connection between the contrary properties: structural instability or distortion out of higher symmetry, a small HOMO-LUMO gap, and paramagnetic response currents. We reveal the symmetry principle that is underlying antiaromaticity by showing an intimate and strict symmetry induced relation between these properties. The principle is mathematically rigorous and can be formulated like: First order (and related) Jahn-Teller distorted molecules out of non-cubic and non-icosahedral point groups are prone to induced paramagnetism in magnetic fields parallel to the main axis of symmetry. We show by the exemplary cases of cyclobutadiene, cyclcooctatetraene, pentalene and manganese trifluoride how this principle works and discuss this new perspective on antiaromaticity. [ABSTRACT FROM AUTHOR]