Compressive strain relaxation of a chemical vapor deposition (CVD) grown graphene overlayer has been considered to be the main driving force behind metal surface step bunching (SB) in CVD graphene growth. Here, by combining theoretical studies with experimental observations, we prove that the SB can occur even in the absence of a compressive strain, is enabled by the rapid diffusion of metal adatoms beneath the graphene and is driven by the release of the bending energy of the graphene overlayer in the vicinity of steps. Based on this new understanding, we explain a number of experimental observations such as the temperature dependence of SB, and how SB depends on the thickness of the graphene film. This study also shows that SB is a general phenomenon that can occur in all substrates covered by films of two-dimensional (2D) materials.