The origin of the even-odd rotational state population alternation in the 16O2(a1Δg) fragments resulting from the ultraviolet (UV) photodissociation of 16O3, a phenomenon first observed over 30 years ago, has been elucidated using full quantum theory. The calculated 16O2(a1Δg) rotational state distribution following the 266-nm photolysis of 60 K ozone shows a strong even-odd propensity, in excellent agreement with the new experimental rotational state distribution measured under the same conditions. Theory indicates that the even rotational states are significantly more populated than the adjacent odd rotational states because of a preference for the formation of the A' Λ-doublet, which can only occupy even rotational states due to the exchange symmetry of the two bosonic 16O nuclei, and thus not as a result of parityselective curve crossing as previously proposed. For nonrotating ozone, its dissociation on the excited B1A' state dictates that only A' Λ-doublets are populated, due to symmetry conservation. This selection rule is relaxed for rotating parent molecules, but a preference still persists for A' Λ-doublets. The A''/A' ratio increases with increasing ozone rotational quantum number, and thus with increasing temperature, explaining the previously observed temperature dependence of the even-odd population alternation. In light of these results, it is concluded that the previously proposed parity-selective curve-crossing mechanism cannot be a source of heavy isotopic enrichment in the atmosphere.