One of the hottest debates in psychology – whether bilingual-monolingual differences exist in cognitive control – is at a stalemate. Here we propose that the stalemate could be broken by shifting the research focus to *why* those differences should emerge. We offer an example of this approach by testing the assumption of current theories of language-control associations that adaptive control is involved in bilingualism, specifically language production. Forty-eight unbalanced Italian-English young adults living in the Milan area completed a variant of the Stroop task known to demonstrate adaptive control and a purely linguistic task manipulated in a similar fashion. Both confirmatory and exploratory analyses showed a clear dissociation between the two tasks, with no evidence of adaptive-control involvement in bilingual language production. Although these results need corroboration, they suggest that adaptive control may not be what might produce bilingual-monolingual differences in cognitive control, and invite a rethinking of relevant theories.