The oxidant is a crucial factor affecting the performance of direct oxidation of methane to methanol (DMTM). It is still extremely challenging to realize one-pot DMTM using dioxygen. So far, hydrogen peroxide is still the most frequently reported green oxidant for DMTM with high selectivity of methanol. Aiming to achieve insights into the influence of oxidants on the DMTM performance and to improve catalysts, we computationally investigated the reaction mechanisms of DMTM using hydrogen peroxide at mono-copper sites in three kinds of Cu-exchanged zeolites with different sizes of the micropores. We identified the common advantage and limitations of hydrogen peroxide as the oxidant. In contrast to molecular oxygen, the O-O bond of hydrogen peroxide could be easily broken to produce reactive surface oxygen species, enabling the facile C-H bond activation of methane at a lower temperature. However, the radical-like mechanism for the C-H bond activation in DMTM using hydrogen peroxide makes the C-H bond breaking of methanol ineluctably superior to methane. This leads to the inevitable trade-off between selectivity and activity for DMTM. Moreover, the lower O-H bonding energy of hydrogen peroxide would also result in the significant self-decomposition of hydrogen peroxide. Despite the existence of these bottlenecks, the kinetic analysis manifests that it is still promising to improve catalysts to boost the performance of DMTM using hydrogen peroxide.