To advance electrochemical H2O2 production and unravel catalytic mechanisms, the precise structural coordination of single-atomic M-N-C electrocatalysts is urgently required. Herein, the Co-N5 site with an asymmetric electronic configuration is constructed to boost the two-electron oxygen reduction reaction (2e- ORR) compared to symmetric Co-N4, effectively overcoming the trade-off between activity and selectivity in H2O2 production. Both experimental and theoretical analyses demonstrate that breaking the symmetry of Co-N sites promotes the activation of O2 molecules and moderates the adsorption of the key *OOH intermediates by disrupting the linear scaling relationship for intermediate adsorption. This modulation enables efficient H2O2 production and its effective retention for subsequent applications. As a proof of concept, Co-N5 achieves a H2O2 production rate as high as 16.1 mol gcat-1 h-1 in a flow cell, outperforming most recently reported counterparts. Furthermore, the coupling of 2e- ORR with the oxidation of cellulose-derived carbohydrates accomplishes high formic acid yields (84.1% from glucose and 62.0-92.1% from other substrates), underpinning the sustainable electro-refinery for biomass valorization at ambient conditions. By elucidating the intrinsic relationship between 2e- ORR and the asymmetry of single-atomic sites, this work paves the way for high-performance electrosynthesis.