The Woodward-Hoffmann (W-H) rule and the Fukui's frontier-orbital theory (FMO) were assessed for the title reactions. Diels-Alder reactions of the normal electron demand were investigated with density functional theory calculations. The C-s symmetry is usually conserved in [4 + 2] reactions between 1,3-dienes and olefins of symmetric geometries. However, those between very nucleophilic dienes and olefins substituted by four electron-withdrawing groups take C-1-symmetry paths. This result is in contrast to the postulate of the W-H rule that the C-s symmetry should be conserved in "symmetry-allowed" paths. A [6 + 4] cycloaddition between tropone and cyclopentadiene was found not to take the C-s-symmetry path despite the symmetry-allowed reaction. Configuration analysis was carried out and gave the magnitude of various orbital interactions. The three-body orbital mixing leads to the symmetry lowering of reaction paths. FMO explains reasonably the anomaly of the cycloadditions of non-W-H rule in strong donor and acceptor reactants and in reactants with nearly degenerate frontier orbitals.