  We study the origin of the stellar $\alpha$-element-to-iron abundance ratio, $[\alpha/\mathrm{Fe}]_{\ast}$, of present-day central galaxies, using cosmological, hydrodynamical simulations from the Evolution and Assembly of GaLaxies and their Environments (EAGLE) project. For galaxies with stellar masses of $M_{\ast} > 10^{10.5}$ M$_{\odot}$, $[\alpha/\mathrm{Fe}]_{\ast}$ increases with increasing galaxy stellar mass and age. These trends are in good agreement with observations of early-type galaxies, and are consistent with a `downsizing' galaxy formation scenario: more massive galaxies have formed the bulk of their stars earlier and more rapidly, hence from an interstellar medium that was mostly $\alpha$-enriched by massive stars. In the absence of feedback from active galactic nuclei (AGN), however, $[\alpha/\mathrm{Fe}]_{\ast}$ in $M_{\ast} > 10^{10.5}$ M$_{\odot}$ galaxies is roughly constant with stellar mass and decreases with mean stellar age, extending the trends found for lower-mass galaxies in both simulations with and without AGN. We conclude that AGN feedback can account for the $\alpha$-enhancement of massive galaxies, as it suppresses their star formation, quenching more massive galaxies at earlier times, thereby preventing the iron from longer-lived intermediate-mass stars (supernova Type Ia) from being incorporated into younger stars. 
The origin of the $\alpha$-enhancement of massive galaxies