Helen: Everyone's special, Dash.
Dash: [muttering] Which is another way of saying no one is.
SYNDROME: And when I'm old and I've had my fun, I'll sell my inventions so that everyone can be superheroes. *Everyone* can be super! And when everyone's super...*no one* will be.
I have no reason to disbelieve Brad Bird, in interviews like this one, when he says that his 2004 INCREDIBLES wasn't informed by any readings of weighty philosophers like Ayn Rand and Friedrich Nietzsche. It's much more likely that he was primarily seeking to invest his big-budget superhero cartoon with as much drama and comedy as he could, the better to impress the "big kids" in the audience. His principal strategy was to take the superhero concept at face value and figure out what made the concept popular, as opposed to reading it as a fascist construction or the like.
As far as THE INCREDIBLES is concerned, the core concept is that of a hero with special abilities or talents rescuing ordinary people from assorted menaces. This was how almost all superheroes and their related congeners were treated in the pulps and comics of the early 20th century. However, in the 1960s Marvel Comic Books spearheaded a new paradigm. Now superheroes still strove to rescue ordinary human beings from danger, but the people didn't always reward their saviors properly, responding instead with pettiness, greed, and superstitious fear.
To my knowledge Brad Bird has never admitted his film's borrowings from Marvel's FANTASTIC FOUR. Though this indebtedness is very likely, it's less important to me than his translation of the Marvel paradigm into a standalone cartoon form. Bird may or may not be familiar with the earliest Lee-Kirby-Ditko breakthroughs, in which petty human responses to superheroes were used largely for comic relief. Yet later comics-writers expanded on these tropes to show the full span of human intolerance, which often led to situations in which superheroes were banned from active service to humankind.
Real superhero comics started out with heroes receiving nearly unconditional accolades for their deeds in the 1940s, and began dealing with more ambivalent responses from the 1960s on. Bird's scenario begins with a time of acceptance, wherein superheroes endlessly contend with super-villains and other threats and win public gratitude, but this period only occupies the first fifteen minutes of the movie's running time.
The period of rejection begins with the film's viewpoint character, Mister Incredible, who becomes the focal point of his world's paradigm shift. In the space of one evening-- when he's scheduled to marry the costumed heroine Elastigirl-- Incredible tries to get in a few more good deeds. The first indication of trouble-to-come is his meeting the obnoxious "Incrediboy," who presumptuously demands that the superhero adopt Incrediboy as his sidekick-- a demand Incredible instantly rejects. The same night, Incredible rescues an attempted suicide. This fortuitously leads him to encounter a crime-in-progress by super-villain Bomb Voyage. But Incrediboy, not one to take "no" for an answer, intrudes, arguing that his special rocket-boots make him fit to join Incredible's crusade, A complicated set of circumstances results in one of the villain's bombs destroying an elevated train-track, though Incredible manages to save the passengers. However, both the attempted suicide and the passengers then sue Incredible for injury-claims. (All are seen wearing neck-collars, which in pop-culture has become code for "phony injury.') These suits lead to the widespread banning of superheroes, who are forced to hang up their capes and live the same ordinary lives as everyone else.
The first quote at this essay's opening is from Dash, youngest child of Incredible and Elastigirl, fretting that he's been forced to conform to an unfair standard of ordinariness. He's what I'll call "the positive face of exceptionalism," which applies to a person who possesses exceptional qualities and seeks to use them well-- be it simply for self-fulfillment, as Dash initially desires, or for the protection of people without such qualities, which is the main orientation of Mister Incredible.
But what does it mean when Syndrome-- the embittered Incrediboy turned super-villain-- expresses the same sentiment? Syndrome, though he's aged fifteen years by the time Mister Incredible encounters him again, is more like a child than Dash ever is: a being of pure ego who has no empathy for victims and merely wants to be lionized. Syndrome plays an indirect role in bringing about the circumstances that exile Mister Incredible from the game of superheroes, but this isn't enough. His ego is so deeply bruised by the rejection that he must eradicate all of the retired superheroes from existence, humiliate and kill Incredible, and eventually become the world's premiere superhero by an act of phony heroism. Thus he's clearly the negative face of exceptionalism, desiring to be seen as the pinnacle of creation. Yet, once he's satisfied himself with duplicating Mister Incredible's popularity with ordinary people, he then plans to put an end to the raison d'etre of superheroes by giving artificial super-powers to everyone.
Since Syndrome is defeated without realizing any of his goals, Bird's story doesn't have to deal with what might or might not happen if the villain succeeded. But the question remains: why would it have been bad, to have a world in which everyone had artificial super-powers?
The answer may lie in the philosophical ruminations of Nietzsche, even if Bird never read him. Nietzsche's ideal of his Ubermensch is not covalent with any version of the superhero, with one exception. the motivation of magnanimity. The Nietzschean "superman" is magnanimous because he has so much more "spirit" than common people. Superheroes generally don't show as much contempt for the rabble as Nietzsche did, but there's still a sense that superheroes are frequently magnanimous for similar reasons. But even here, there's a crucial difference. Mister Incredible enjoys getting praise and plaudits for his super-deeds, but his deeds primarily spring from empathy: from the realization that ordinary people need his help. Syndrome has no motivation beyond lionization, and so it's easy for him to restructure the world so that it reflects his own mediocrity. Once everyone has access to artificially-enhanced superpowers, will anyone feel any need to feel empathy for those weaker than themselves?
Lastly, the opposition of "natural powers" and "artificial powers" begs some consideration. The only real superheroes the viewer sees are the four Incredibles and their family friend, Frozone; any others get only brief references. These five seem gifted with "natural" powers, though, because Bird provides no origin-stories, there's no knowing if they were all born with their powers like Dash and Violet. When Incrediboy makes his second audition to be Incredible's sidekick, he claims that not all superheroes have super-powers, meaning that there may be analogues to Batman and the Green Hornet in Bird's world. But this sort of niggling would have distracted from Bird's main theme: the opposition between that which is ordinary and that which is "super" or "special." Syndrome, with his plethora of weapons, is first and foremost an evocation of classic super-villains like Luthor, able to unleash a never-ending series of challenges to a hero or group of heroes. (It's also worth mentioning that a fellow named Xereb, rather than Syndrome, was originally going to be the movie's main villain, until the character of Buddy/Incrediboy impressed people enough to rework him into Principal Villain.) There's no suggestion that artificial enhancements are wrong when used for good purposes: the whole idea of Edna, costume-maker to the superheroes, depends on her being able to pursue her own ideals of excellence with the use of technological items like expanding fabric and invisibility cloth.