The difficult thing about satire is that, on the surface, it can look almost identical to sarcasm and insults. In fact, many times satire actually uses sarcasm to make its points, however there's a key difference. While sarcasm and insults are only used as a form of attack (for the subject matter) or personal gain (for the attacker), satire is less about the destruction and more about the identification of the flaws. In fact, though it may seem cruel, satire is actually using insults and sarcasm for a greater good. Whether it's to bring awareness of a flaw, or show others the foolishness of their language, satire can be a powerful tool in getting people to step back and look at their reality in a new way. Sarcasm, however, is usually only good for a one-liner or two, and insults, while clever, aren't designed to build anything.
That is probably the reason we teach satire in school in the first place, and probably why, even though it's one of the most approachable genres, its also one of the most difficult for students to actually grasp...mainly because many students (and many adults) for that matter, don't think about the world deeply. The same crowd that likes to read a book and considers it "just a story about a guy who wants to be king" is unlikely to think deeply about society either. Perhaps that's satire's biggest advantage: regardless of your opinion, it makes you think just a little harder.