We present ab initio calculations examining two previously proposed mechanisms for H-2 desorption from the Si(100)-2 X 1 monohydride phase: (i) the ''prepairing'' mechanism, where H-2 desorbs directly in a one-step process via two hydrogen atoms paired on one silicon dimer and (ii) a stepwise mechanism in which H-2 desorbs from a dihydride intermediate formed via isomerization of the monohydride. Both pathways are predicted to be 66 kcal/mol endothermic. A detailed search of the transition state region rules out the direct one-step mechanism, as only one saddle point was found and a search of the reaction path showed that it evolves from the dihydride intermediate rather than the monohydride. This saddle point for the second pathway corresponds to a desorption activation barrier of 94 kcal/mol, which is much higher than those measured by thermal desorption experiments (45-66 kcal/mol). Other prepairing desorption pathways involving H-2 desorption from two neighboring hydrogen atoms on adjacent dimers are argued to be inconsistent with the observed first-order kinetics. Thus, no previously proposed mechanism appears consistent with both the observed barrier height and reaction order. We propose an alternative mechanism involving H atom diffusion prior to H-2 desorption. In particular, our calculations suggest two constraints on the mechanism: (i) H-2 must desorb from a SiH2(a) species that either has no memory of how it was formed or is formed by means of a step no more than approximately 10 kcal/mol endothermic and (ii) H atom surface diffusion to form SiH2(a) plays a key role in determining the reaction orders on different Si surfaces. Our results indicate that H-2 always desorbs solely from SiH2(a), independent of theta(H) or surface structure. At low coverages (theta(H) less-than-or-equal-to 1 ML), where the monohydride phase is present, the activation barrier for H-2 desorption from SiH2(a) is predicted to be 55 kcal/mol. We predict that the activation barrier decreases with increasing theta(H), reaching a minimum of 38 kcal/mol at theta(H) = 2 ML, in good agreement with experiment.