The desire to skip ahead to “critical thinking” is most clearly a desire for logic: seeing what follows logically from what, spotting a bad inference, and being clear about one's potential biases. This is obviously a good thing. Someone who cannot tell a contradiction from a mere disagreement will likely have many problems in ordinary life just as in the sciences. Sometimes, however, critical thinking goes beyond logic and seems to make implicit claims about what kinds of things we can know. Courses on critical thinking tend to give criteria by which students can make judgments about claims across the various disciplines. There is nothing wrong with that in principle, but, very often in our time, the tenor and direction of these criteria are that no source can be trusted, everything must be doubted, and all efforts to teach or inform are distorted by underlying goals related to the author's politics. These are not part of the art of reasoning itself; they are conclusions based on other disciplines, and as such they must be evaluated and proved within those disciplines themselves first. And this is what is rarely if ever done for students in critical thinking courses: they are taught criteria from other disciplines and given examples of how they have been applied but those criteria are not proven to the students and so the students are left just trusting yet another set of rules and examples, without a complete account of reasoning and its goals.
Grammar, as it is often taught nowadays, can seem to be a list of corrections and rules and arbitrary preferences. If that is what “grammar” means, the thought that it is not something that needs to be put first when we turn to higher studies makes sense. The same is true of rhetoric, at least in some parts. Many things in rhetoric do, of course, seem relevant to critical thinking, like knowing how others are trying to persuade us, but much of it may seem unnecessary. Why should we consider in detail the parts of a speech and things like rhetorical figures? It can seem better to go straight to logic, and in particular practical logic looking at real arguments and puzzles.
It can certainly be profitable to examine detailed arguments about real subject matters, especially if students are not going to take a more formal course in logic; this is often the best substitute. But an informal course cannot resolve the deeper questions and at least some of the examples will require an answer about how reasoning really works at the most fundamental level. If that deeper level never gets explained, then students are left with just a course that teaches yet more rules and examples, rather than a course that shows them why reasoning must be one way rather than another.
Puzzles and brain-teasers can give us a first taste of reasoning and necessity: if these premises are granted, that conclusion follows from them necessarily. A grid in a logic game, where we have to meet many different conditions to work out who went where and when, requires real reasoning and real inference, even if it is not studied systematically. An interest in logic games and puzzles is a first step toward being drawn into the art of reasoning itself; puzzles like these can be one of the ways a student first feels that thinking requires real discipline, something determinate and fixed.
Beginning with critical thinking and “informal logic”, then, can certainly be good but it has clear limits; there is a great deal more to reasoning than the desire to think critically and avoid mistakes.
The art of reasoning well, however, depends on our ability first to be clear about our words and to use them well and precisely; more than that, we need to know how words come to mean what they mean and how different languages express the same truth differently; one of the effects of a course in critical thinking is that the students ideally become more precise and careful in their use of language and more nuanced in their ability to read and understand others; but that is the goal of the art of grammar itself. Even beyond logic and grammar, our efforts in critical thinking point toward a further art, the art of persuasion. In short, too often modern critical thinking courses are an attempt to replace the trivium itself with a short overview of examples and rules that are supposed to guide and help the students. That is, of course, good. But what is better is the direct study of the arts of grammar, logic, and rhetoric themselves.