The extrinsic antiaromaticity of archetypal cyclobutadiene (CBD) is addressed with particular emphasis on the sigma-pi separability problem. The destabilization energy E(d)(CBD) of CBD is obtained by appropriate homodesmotic reactions involving the open chain zigzag, polyene(s). It is shown that E(d)(CBD) does not depend on the electron correlation and the zero-point vibrational energy contributions, since they are small and of the opposite sign. Consequently, they cancel in the first approximation. Further, it turns out that E(d)(CBD) can be estimated accurately enough with a very modest cc-pVDZ basis set at the Hartree-Fock (HF) level. The extrinsic antiaromatic destabilization E(ean)(CBD) of CBD is deduced after extracting the angular strain energy estimated to be 32 kcal/mol. The resulting E(ean)(CBD) value of 52 kcal/mol is in excellent agreement with the experimental thermodynamic data. If the E(ean)(CBD) is estimated relative to two isolated C=C double bonds, then it assumes 38 kcal/mol, which is roughly 10 kcal/mol per one pi electron. It is, therefore, safe to state that extrinsic antiaromaticity of CBD is larger than its angular strain. Although the sigma and pi electrons are coupled by a mutual Coulomb interaction V-ee(sigmapi), several attempts of their decoupling is made by using three partitioning schemes: stockholder, equipartition, and standard pi-electron theory recipe. The latter allocates the V-nn and V-ee(sigmapi) terms to the sigma- and pi-electron frameworks, respectively. The nuclear repulsion term V-nn is dissected into sigma and pi components in the former two partitioning schemes by using stockholder criterion. It appears that the extrinsic antiaromatic destabilization E(ean)(CBD) is determined by the pi-electron framework according to all three partitioning models.