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By numerically solving the non-Born–Oppenheimer time-dependent Schrödinger equation of H _2 exposed to an isolated EUV laser pulse, we demonstrate the photoionization associated with the 2 sσ _g and 3 pσ _u dissociative states of ${\mathrm{H}}_{2}^{+}$ . The two asymptotically degenerate pathways with opposite parities may interfere and end up with the same kinetic energy release, resulting in the asymmetric electron localization on two nuclei. Due to dipole selection rule, the emitted photoelectron has the opposite parity with the associated ${\mathrm{H}}_{2}^{+}$ , and thus is also on the coherent superposition of states with odd and even parities, leading to the asymmetric directional emission of the photoelectron. The asymmetry is fundamentally determined by the phase difference of the 2 sσ _g and 3 pσ _u dissociation channels.