In this Letter we call into question the perturbatively parity breakdown at 1-loop for the massless QED3 frequently claimed in the literature. As long as perturbative quantum field theory is concerned, whether a parity anomaly owing to radiative corrections exists or not shall be definitely proved by using a renormalization method independent of any regularization scheme. Such a problem has been investigated in the framework of BPHZL renormalization method, by adopting the Lowenstein–Zimmermann subtraction scheme. The 1-loop parity-odd contribution to the vacuum-polarization tensor is explicitly computed in the framework of the BPHZL renormalization method. It is shown that a Chern–Simons term is generated at that order induced through the infrared subtractions — which violate parity. We show then that, what is called “parity anomaly”, is in fact a parity-odd counterterm needed for restauring parity.