The desire to skip ahead to “critical thinking” is often a desire for what logic really is: seeing what follows from what, spotting a bad inference, being clear about one's potential biases. This is obviously a good thing. A mind that cannot tell a contradiction from a mere disagreement is already in trouble, in politics as in geometry.
School grammar, as many students learn it, can seem to be a list of corrections disconnected from any question worth asking. If that is what “grammar” means, the impulse to skip it makes sense; the same is true of rhetoric in at least some of its aspects; of course, some do seem relevant to critical thinking, like knowing how others are trying to persuade you; but much of it may seem simply unnecessary. Why linger over parts of speech and rhetorical figures when there are many claims and arguments that we need to evaluate?
Puzzles and brain-teasers can give us a first taste of reasoning and necessity: if these premises are granted, that conclusion is not optional. A grid in a logic game, where you have to meet many different conditions to solve who went where and when is real reasoning and real inference, even if it is not studied systematically. A concern for logic games and puzzles is a first step toward being drawn into the art of reasoning itself. Puzzles like this can be one of the ways a student first feels that thinking has a discipline, something determinate and fixed.
What is right, then, is the desire to reason well and avoid mistakes; but there is a great deal more than this, both in what we can be clear about and even in what strategies we can learn to help us become our best. But the art of reasoning well is itself dependent on first being clear about our words, how they come to mean what they mean, and how to use them correctly in sentence and paragraph; and the art of reasoning itself points toward a further art, one of persuasion.