This study investigates the influence of transition metal magnetic moments on the adsorption and reactivity of molecular oxygen (O2) in nitrogen-doped graphene-supported single-atom catalyst systems using density functional theory calculations. We demonstrate that metals with higher magnetic moments, such as Cr and Mn, exhibit enhanced affinity and stabilization of O2 adsorption. In contrast, metals with lower or null magnetic moments, like Ni and Cu, show diminished capability to adsorb O2 effectively. Our analysis of adsorption energies, Morse potential depths, and reaction force underscores the critical role of transition metal magnetic moments in dictating catalytic performance and characterizing the nature of the chemical bond between the metal center and oxygen. It has been found that the strength of the oxygen-metal bond as well as its electronic activity are crucial elements that can be used to enhance the catalytic effect in capturing O2. This provides insights for optimizing single-atom catalysts (SACs) in oxygen reduction reactions and other energy conversion applications.