There seems to exist this technocratic fancy about "critical thinking." As if it were a discrete group of rules which could be cultivated in students by simply sitting them down in a classroom, lecturing to them about the rules, and then asking them to apply them in practice scenarios. This, of course, is how one teaches grammar, and most normal subjects.
But would such a student actually become a critical thinker? Or would they simply become a regurgitator of logical fallacies, able to spot them in encountered arguments, but not able to discern whether the reasoning was ACTUALLY fallacious? Take, for instance, the "slippery slope" fallacy. Which is not necessarily a fallacy, because "doing A will lead to B" is valid if both A and B stem from the same principle C. If affirming A implies affirming its principle C, and if B is related to principle C in the same manner as A, then yes, "doing A will lead to B" is valid reasoning.
This is certain value in studying philosophy generally, and formal logic specifically. But it is not a fundamental subject in the same way that most HS subjects are, and it will be of no avail to students who have not already reached a high level of reasoning.
The mistake Paul and other technocrats make when calling for "critical thinking" is that they treat it as an actual subject matter. But there is not textbook for "critical thinking," with which a teacher can instruct a class. It is an intellectual virtue, like curiosity, or honesty. It is not taught directly, but indirectly, through other subjects. THROUGH the constraints and methods of science, one learns to think critically about evidence and causation. THROUGH reading and analyzing literature, one learns to detect intentions, both explicit and implicit, in the voices it encounters. THROUGH algebra and calculus, one learns to think about abstract objects and their relationships.
There is no "shortcut" to critical thinking, just like there is no shortcut to teaching children to be responsible or caring or hardworking. It is a skill that has to be practiced in the various arenas of life.