Song in birds is produced by the syrinx, a vocal organ at the junction of the bronchi, and in most temperate songbirds the neural circuits controlling it are strongly enlarged in males under the influence of testosterone. Female song was long treated as an oddity. It is not. Reconstruction of songbird ancestry indicates female song was present in the common ancestor of songbirds and has been lost repeatedly rather than gained.
Cardinals make the point plainly. The female sings from cover near the nest, often a longer phrase than the male's, and pairs counter-sing by matching each other's song types. Observers have long linked female song near the nest with the male's provisioning behaviour, though the specific claim that it signals a food request has not been established with controlled evidence.
What is settled is that both sexes have a shared repertoire and sing from the same learned pool. The old field-guide shorthand that a singing cardinal is a male is simply wrong, and it survives mostly because the red male is easier to see.