The mechanism of unburnt pocket formation in an unsteady two-dimensional premixed lean methane-air flame is investigated using direct numerical simulations. Theoretical results for nonlinear diffusion equations combined with analytical examples are used to interpret some of the results. Flame structure and propagation show three distinct stages of pocket formation: (1) flame channel closing involving head-on quenching of flames, (2) cusp recovery, and (3) pocket burnout. The flame channel closing and subsequent pocket burnout are mutual annihilation events that feature curvature, diffusion normal to the flame front, unsteady strain rate effects, and singularities in fame propagation and stretch rate. The results show that during channel closing and pocket burnout thermo-diffusive and chemical interactions result in the acceleration of the flames prior to annihilation; the time scales associated with the final stage of mutual annihilation and the initial stage of cusp recovery are significantly smaller than diffusive and convective time scales. As in earlier one-dimensional studies, the acceleration is attributed to enhanced diffusion and reaction rates, modifications to species profiles leading to shifts in balance between diffusion and reaction, and vanishing species and thermal gradients at the location in the channel where the pocket pinches off. Flame propagation and stretch rate are singular at this location. Enhanced radical production is initiated by a reversal of diffusion of H-2 towards the reaction zone during the early stages of thermo-diffusive interactions. Peak radical concentration resulting from flame channel closing and pocket burnout exceed peak laminar values by as much as 25%. After the merging of the fuel consumption layers, radical production and flame structure shifts more towards an H-2/CO/O-2 system at the expense of hydrocarbon reactions. Species thermodiffusive interaction times are shorter than the unstrained one-dimensional counterpart due to unsteady strain and convection. Curvature effects on the flame propagation are prominent during pocket burnout and cusp recovery. The recovery stage shows strong dependence on diffusion of radicals left from the channel closing stage. This diffusion is amplified by the strong curvature of the flame cusp.