The case for including fallacies in teaching critical thinking is weaker than it seems. Further, there are at least four arguments against using fallacies as a framework for teaching critical thinking. Empirical research is needed to determine what kinds of mistakes in reasoning occur most commonly in arguments and what effect teaching the fallacies has on critical thinking dispositions and skills.
Hitchcock, D. (2017). Do the Fallacies Have a Place in the Teaching of Reasoning Skills or Critical Thinking? In Argumentation Library (Vol. 30, pp. 401–408). Springer Nature. https://doi.org/10.1007/978-3-319-53562-3_25