There is a great and eternal need for Antony Flew's kind of common sense, because it isn't common at all.
Mr. Flew is all about bad reasoning. The kind of bad reasoning presented to us by newspaper editorial writers, political speakers, and advocates for all sorts of programs and policies, left, right, and center. It isn't that hard to think critically. One doesn't need a lot of education or special training, although a book like How to Think Straight could certainly help. I found on rereading How to Think Straight that I was reminded of a great many evasions and fallacies that I see almost every time I pick up an issue of Mother Jones, or Commentary, or Foreign Affairs, or the Atlantic.
A constant alertness to the possibility that someone is trying to tell you that something in proven, that they know something, when they in fact don't know it at all. They may believe it, but belief is a much lower standard than knowledge.
I like two particular fallacies: The Genetic Fallacy, in which one asserts that something is from its origin that into which it will develop. This shows up going in either direction. You have authors such as Desmond Morris asserting that, because we evolved from something like an ape, that we are still apes. And yet, he recognized that we have evolved, so we can't still be merely apes. In the other direction, you have the anti-abortionists asserted that a cluster of four or eight cells is a human being, with all the rights thereto appertaining. An acorn is not an oak tree, and an oak tree is not an acorn.
The Naturalistic Fallacy is the move of going directly from "is" to "ought." There is a whole body of literature, going back to Aristotle's Nicomachean Ethics, establishing the point that no set of facts creates a moral obligation. You need a preexisting maxim to which you can compare the current set of facts.
Great book! Highly recommended for anyone who wishes to write, to speak, or just to understand how the fellow on television is trying to mislead us.