"Alternative facts" have gotten quite a bad rap lately, which — while understandable — is a shame. Because virtually any argument worthy of the name involves competing sets of facts. That's why it's an argument, not a hug-fest. And to pretend otherwise is actually counterproductive, especially if we want our students to be able to engage in constructive arguments.
Take trial lawyers, for example. To exonerate their clients, defense attorneys often present alternative theories, based on alternative facts, most of which are actually facts. Perhaps the accused can prove he was never at the crime scene, even though his blood was found on the victim. In its deliberations, the jury must weigh these seemingly disparate facts — although what they may really be judging is which lawyer made the better argument. Much the same is true of political debates.