<p>The easily accessible anonymous misinformation in social networks makes critical thinking vital to identify weak evidence, fallacies, or misleading sources. To assess the credibility of information, reading comprehension seems to be key, together with the argumentative capacity. To argue well, we need dual-function argumentation, that is, arguing in support of the favored option and counterarguing against it. This study aimed to analyze secondary school students and pre-service teachers’ dual-function argumentation—the practice of presenting and reasoning through both sides of an argument, measured through the quality of their justification of the credibility of a fake news item. It also aimed to explore the relation between the participants’ credibility, their reading comprehension, and the quality of their argumentation. The quality of dual-function argumentation was low in both samples. Only 16% of the students included a counterargument in their texts and none of them included a rebuttal. Thirty percent of the pre-service teachers included a counterargument, but just 6% included a rebuttal. Furthermore, the less the students believed the news, the better their argumentative competence, whereas this relation was not found in pre-service teachers. Finally, reading comprehension played a role in both credibility and quality of argumentation. Training on how to manage fake news is specially needed among our future teachers to enhance students’ argumentative capacities to address misinformation.</p>