Ultraluminous infrared galaxies (ULIRGs) show on average three times more emission in the rotational transitions of molecular hydrogen than expected based on their star formation rates. Using Spitzer archival data, we investigate the origin of excess warm H-2 emission in 115 ULIRGs of the IRAS 1 Jy sample. We find a strong correlation between H-2 and [Fe ii] line luminosities, suggesting that excess H-2 is produced in shocks propagating within neutral or partially ionized medium. This view is supported by the correlations between H-2 and optical line ratios diagnostic of such shocks. The galaxies powered by star formation and those powered by active nuclei follow the same relationship between H-2 and [Fe ii], with emission line width being the major difference between these classes (similar to 500 and similar to 1000 km s(-1), respectively). We conclude that excess H-2 emission is produced as the supernovae and active nuclei drive outflows into the neutral interstellar medium of the ULIRGs. A weak positive correlation between H-2 and the length of the tidal tails indicates that these outflows are more likely to be encountered in more advanced mergers, but there is no evidence for excess H-2 produced as a result of the collision shocks during the final coalescence.