Copper, obtained from porphyry deposits formed in arc settings, is a critical resource, and is primarily sourced from magmas. However, the processes that shape the copper contents of arc magmas are up for debate. Existing models place emphasis on different petrological agents that explain large-scale trends in copper systematics. Previous studies have noted the ’Cu paradox,’ where the magmas with high Sr/Y ratios, indicative of ore-forming potential, have the lowest copper concentrations. Here we compile a multidimensional database of volcanic whole rock compositions and couple it with simple petrological models to elucidate the controls on volcanic whole rock compositions with respect to Cu. We show that calc-alkaline, high Sr/Y magmas undergo major element modification caused by extensive amphibole and/or garnet fractionation, which promotes sulphide precipitation and copper depletion. We demonstrate the importance of amphibole fractionation as a globally important process that promotes both calc-alkaline differentiation and sulphide fractionation in arc magmas, as well as its role in signalling the right set of chemical conditions in magmas that ultimately feed copper porphyry deposits. This work also raises the possibility of amphibole as a geochemical and petrological indicator of potential porphyry-forming conditions in a magma, which we show should be readily detectable by a combination of different geochemical metrics. Despite their paucity in copper, high Sr/Y magmas are associated with porphyry deposits, implying that the propensity of magmas to form such deposits depends on factors other than a magma's bulk copper content.