Critical discourse on large language models (LLMs) has bifurcated between epistemic dismissal that invokes some form of the stochastic parrot metaphor to puncture hype, and pragmatic accommodation that treats LLM capability improvements as grounds for updating the critique. We argue that both misdiagnose the problem as the issue is not whether or not LLMs work, but what kind of working is happening and at whose cost. Drawing on meta-theoretical frameworks of cognitive science, feminist labor analysis and critical pedagogy, we propose a conceptual reorientation. We develop this claim through registers of (i) the cognitive, examining what is forfeited when statistical pattern-matching substitutes for the iterative, grounded processes that constitute thinking; (ii) the pedagogical, examining how “AI literacy” as currently deployed is itself a symptom of the confusion it purports to address; and (iii) the political, examining how the infrastructure framing of AI naturalizes asymmetric labor displacement, particularly of feminized cognitive and reproductive work. The stochastic parrot, deployed with mechanistic precision rather than mere rhetorical convenience, specifies what is forfeited when cognitive labor is delegated, who bears the cost, and why a literacy adequate to this moment must begin from the epistemology of those most harmed by the systems it describes. We conclude with underlining that critical AI literacy, which this paper embodies an instance of, is the only sensible way forward.