College courses in logic traditionally spend some time talking about fallacies, often identifying them by nifty-sounding Latin names. For example, an argumentum ad hominem (literally an argument "to the person"), is attack on another person's character rather than a response to what they're saying, and an argumentum ad ignoratium ("to ignorance") amounts to declaring that if the other side can't prove you wrong, you must be right. There are many lists of fallacies on the Internet, such as this one.
Even better, read Max Shulman's hilarious short story "Love Is a Fallacy," one of his series about college student Dobie Gills. In this story Dobie decides that his life goals require having a smart and beautiful wife, and since he's not sure he can find that combination ready-made, he determines to start with a beautiful girl and teach her to be intelligent by educating her in logic. It's often reprinted in logic textbooks, and if you haven't yet read it, you really owe it to yourself to find it on line. There's a PDF here, for example. Seriously, it's worth the few minutes it will take you to read it.
(The classic television series The Many Loves of Dobie Gillis (1959-1963) had an episode with the same name, but the plot is quite different.)
One of the lesser-known fallacies is argumentum ad verecundiam, meaning an appeal to authority (literally to "reverence"). The idea is that an authority having said something doesn't constitute absolute proof, because authorities can be wrong. This has obvious appeal to those who don't want to believe what experts tell them and prefer to believe what they want to believe, but that's if anything even less logical.
Recently Hank Green posted something very intelligent and succinct about paying attention to experts on the vlogbrothers channel, and I think it's worth the three or four minutes it takes to watch: