A longstanding assumption within higher education is that there is a clear link between argumentative writing and critical thinking. In this paper, I challenge this assumption. I argue that argumentative writing genres of persuasion, inquiry, and consensus fail to target students' open-mindedness, which is an important aspect of critical thinking. In particular, argumentative writing genres do not challenge students to confront key cognitive biases, namely confirmation bias and motivated reasoning, when engaging in moral, political, and/or social questions. The motivation to conduct a balanced selection of evidence as well as an unbiased interpretation of evidence is overshadowed by the motivation to preserve one's prior beliefs. The structure of argumentative writing genres thereby stifles open-mindedness and can even nurture dogmatism. As a result, in our goal to develop students' critical thinking skills through argumentative writing, we may be doing more harm than good.