The role of spin non-adiabatic effects in the reactivity of O₂ on metal surfaces has been a matter of debate for several years. By means of density functional theory with a semi-local exchange–correlation functional, and classical dynamics calculations, we show that the recently observed activated character of O₂ adsorption on Cu(111) and Cu_ML/Ru(0001), as well as the delicate interplay between dissociative and non-dissociative O₂ sticking on Cu(111) at different surface temperatures, can be explained by assuming an adiabatic evolution of the molecular spin. This suggests that spin adiabaticity during O₂ adsorption on metal surfaces could be a more general scenario than anticipated.