Natural language misinformation detection approaches have been, to date, largely dependent on sequence classification methods, producing opaque systems in which the reasons behind classification as misinformation are unclear. While an effort has been made in the area of automated fact-checking to propose explainable approaches to the problem, this is not the case for automated reason-checking systems. In this paper, we propose a new explainable framework for both factual and rational misinformation detection based on the theory of Argumentation Schemes and Critical Questions. For that purpose, we create and release NLAS-CQ, the first corpus combining 3,566 textbook-like natural language argumentation scheme instances and 4,687 corresponding answers to critical questions related to these arguments. On the basis of this corpus, we implement and validate our new framework which combines classification with question answering to analyse arguments in search of misinformation, and provides the explanations in form of critical questions to the human user.