Critical thinking is supported by a rich and diverse literature, with particularly close ties to argumentation theory and informal logic. It has often been presented in terms of a set of skills and dispositions, with the latter exemplified through the figure of an ideal critical thinker. These accounts of the relevant dispositions are intuitive and tend to emphasize openness, clarity, and a concern for truth. Seemingly running against this impression, it is argued here that an ideal critical thinker can willfully engage in fallacious argumentation. This surprising possibility is grounded in the distinction between thinking and arguing, with the literature on critical thinking being implicitly and rightly limited to the former. The argument draws on an established account of critical thinking dispositions, a simple supporting view of the nature of dispositions, and analogies to familiar phenomena like lying. The result complements existing work on the subject in terms of what a critical thinker should do, contributing to our understanding of the conceptual boundaries of critical thinking and argumentation proper.