ABSTRACT Many disc galaxies in clusters have been found with bulges of similar age or younger than their surrounding discs, at odds with field galaxies of similar morphology and their expected inside-out formation. We use the Evolution and Assembly of GaLaxies and their Environments (EAGLE) simulations to test potential origins for this difference in field and cluster galaxies. We find, in agreement with observations, that on average disc-dominated field galaxies in the simulations have older inner regions, while similar galaxies in groups and clusters have similarly aged or younger inner regions. This environmental difference is a result of outside-in quenching of the cluster galaxies. Prior to group/cluster infall, galaxies of a given present-day mass and morphology exhibit a similar evolution in their specific star formation rate (sSFR) profiles. Post-infall, the outer sSFRs of group and cluster galaxies significantly decrease due to interstellar medium stripping, while the central sSFR remains similar to field galaxies. Field disc galaxies instead generally retain radially increasing sSFR profiles. Thus, field galaxies continue to develop negative age gradients (younger discs), while cluster galaxies instead develop positive age gradients (younger bulges).