Then the next move of a critical thinker would be to point out the respects in which this analogy doesn’t hold, and so demonstrate how poor it is at supporting the conclusion provided.
In recent years, it’s been very common to include discussion of cognitive biases—the psychological mistakes we make in reasoning and the tendencies we have to think in certain patterns which don’t give us reliably good results.
That’s another aspect: focussing on the cognitive biases is a part of what’s sometimes called ‘informal logic’, the sorts of reasoning errors that people make, which can be described as fallacious. Some of them are simply psychological tendencies that give us unreliable results.
But one of the ways of doing it is to have memorable labels, which can describe the kind of move that somebody’s making, or the kind of reasoning error, or the kind of persuasive technique they’re using.
For example, you can step back from a particular case and see that somebody’s using a ‘weak analogy’.