It is shown that the puzzling experimental observation of suppressed molecular ionization, in intense laser fields, of O2, and its absence in N2, is a symmetry induced dynamical effect. More generally, it is predicted that the ionization signal of the class of homonuclear diatomic molecules having valence orbitals with an antibonding symmetry (e.g., sigma(u), pi(g)) would be suppressed, but not those with a bonding symmetry (e.g., sigma(g), pi(u)). The suppression effect can be visualized as due to an effective destructive interference between the two subwaves of the ionizing electron emerging from the two atomic centers.