Microbes have the potential to be highly cooperative organisms. The archetype of microbial cooperation is often considered to be the secretion of siderophores, molecules scavenging iron, where cooperation is threatened by "cheater" genotypes that use siderophores without making them. Here, we show that this view neglects a key piece of biology: siderophores are imported by specific receptors that constrain their use by competing strains. We study the effect of this specificity in an ecoevolutionary model, in which we vary siderophore sharing among strains, and compare fully shared siderophores with private siderophores. We show that privatizing siderophores fundamentally alters their evolution. Rather than a canonical cooperative good, siderophores become a competitive trait used to pillage iron from other strains. We also study the physiological regulation of siderophores using in silico long-term evolution. Although shared siderophores evolve to be downregulated in the presence of a competitor, as expected for a cooperative trait, privatized siderophores evolve to be upregulated. We evaluate these predictions using published experimental work, which suggests that some siderophores are upregulated in response to competition akin to competitive traits like antibiotics. Although siderophores can act as a cooperative good for single genotypes, we argue that their role in competition is fundamental to understanding their biology.