A coupled socioeconomic-energy system has not been linked to the carbon emission trajectory of a country to uncover its role in peaking emissions. Targeting typical developed countries having peaked carbon emissions covering 10 years before and after the emission peak, we measure the coupling between two systems and probe its influencing mechanism on peaking emissions. Results indicate that two systems have both better interaction and quality in the developed countries, with the coupling level and coordination level both greater than 0.85. A consistency lies in the trends in comprehensive coupling level and emissions, analogizing to the emission peaking trajectory. The best coupling state for two systems facilitates the emission peak. The comprehensive coupling level for the developing countries evolves upward steadily, driven by the increasing development level of two systems that have not arrived at the best coupling state, which explains why the emissions have not peaked.