Argumentation

Relevance to everyday reasoning situations and political discourse in a democratic society
Instructors may learn something (given the recent flourishing of argumentation scholarship) which may contribute to their own scholarship

Instructors may have to master new material (given the recent flourishing of argumentation scholarship)
Other skills may be important for everyday reasoning, e.g. interpreting statistics and tables for citizenship, or formal logic for philosophy majors. Other forms of critical thinking include problem-solving and specific disciplinary methodologies.

Some texts still neglect presumptive argumentation schemes (e.g., analogical reasoning and causal reasoning) and fall back on the inadequate categories of inductive and deductive inference.
If you want to teach fallacies, consider a textbook that focuses on them. I advise against the common strategy of a separate few days or weeks covered in separate chapters; either integrate fallacies or don’t teach them at all. To include fallacies in a larger context, look for a text that treats fallacies alongside inference/argumentation schemes, e.g. Epstein; Boss; Woods, Irvine and Walton.

Ralph H. Johnson and J. Anthony Blair. Logical Self-defense; US edition again in print from IDEA. A fallacies-based approach that also provides one of the best accounts of argument diagramming.