Science fiction is about ideas. It's about the exploration of a concept in science or technology and seeing its effect on society. What is the idea behind Star Wars?
If you ignore the science fiction setting, the Star Wars movies don't deal with science fiction issues very much. They deal with the battle between good and evil, which are differentiated quite clearly. There's very little middle ground. As well, this battle between good and evil is what sets off the action. These movies are much more like a fantasy story in a science fiction setting.
How could I claim that Star Wars is fantasy? The main heroes fight with swords (mostly). The heroes (and a couple of villains) use a magical power to gain an advantage over most of their enemies. At best, the struggle is a conversation about what kind of government is better for a galaxy, a dictatorial bureaucracy or a looser, more democratic system. Interestingly, the movies make a point that the dictatorial bureaucracy is much more efficient than a democracy, an important theme of the three prequel movies where the initial democracy is seen as inefficient and corrupt. Yet this argument tends to fall apart because we never really see what kind of government replaces the empire. At the end of The Return of the Jedi the evil emperor had been defeated, but we don't see what kind of government the rebels replace the empire with.
The best science fiction idea from Star Wars is probably the concept of the Death Star. Unfortunately, the idea of a weapon so strong it can destroy another planet isn't really a new one, nor is presented in a particularly innovative way. A better example of this might be the classic Star Trek episode “The Doomsday Machine”, where an automated “planet killer” is roaming through our galaxy, munching on planets (and star ships) for fuel. Its hull is impenetrable, which makes it a very difficult thing to kill. It's certainly nothing a lone snub-fighter could destroy, with a precision attack on a stupid design flaw.
Where Star Wars does become science fiction is in its setting, yet I would argue that may not be enough to make it a science fiction story. The different planets in the Star Wars universe are well-researched in terms of their ecosystems. As well, the space ship designs employ a certain wild creativity that makes them fascinating to look at. At best, Star Wars is the kind of science fiction called space opera, a type of science fiction story that emphasizes adventure and romance. We have lots of examples of space opera, from the Buck Rogers/Flash Gordon stories to the novels of E.E. “Doc” Smith and the the John Carter, Warlord of Mars books by Edgar Rice Burroughs. These stories are fun but not really “serious” in the same sense of H.G. Wells. Star Wars certainly isn't as goofy as some of the Buck Rogers stories (or as racist), but it shares this genre's focus on melodrama and adventure.
So when you talk about science fiction in your classrooms, keep in mind that the most recognizable example of the genre barely fits within the genre.
The classic Star Trek episode “The Doomsday Machine”, written by Normal Spinrad.
The Star Wars movies, episodes 4–6, and 1–3 (regretfully)