The movie is very clear. The villian's nefarious plan is to sell the inventions that make him super so that everyone can have them. This will make everyone super, which, he reasons, is the same as no one being super. This is clearly presented as 1) logical, and 2) a scary idea. We can't have everyone being super! The viewer is supposed to hear this and feel resentful on behalf of the Incredibles family, because they're REAL superheroes, and they're SPECIAL, and now this guy is going to take that away by making everyone else just as good as them!
The Parrs and the other superheroes
are more deserving of their powers; they use them for the common good with no thought of reward for themselves. It matters not one hill of beans if they worked to gain those powers or were born with them. The whole point is that they took a gift that made them better in some way than most people and learned to use it responsibly and for the benefit of others. Since being good is almost always much harder than being selfish, in becoming deserving of those powers they were born with they worked a lot harder than most others ever work in their lives, at anything.
Syndrome's idea is a titanically dangerous one because he'll supply powers to anyone with money to pay for them. The vast majority of people are not going to be so selfless as the heroes; Syndrome would basically create a huge tide of supervillains or a huge tide of people who'd instantly kill themselves because they can't be bothered to read a manual, and laugh all the way to the bank while doing it. It would be like handing a gun to a baby.
The point of the movie really resides with Dash. He's the first person to use this phrase. He's a kid and can't see why he can't use his natual gift (which, unique among the Parrs, is the only thing
everyone can do - he can just do it way better than most) to gain things it would be impossible for others to attain.
Robert, whose life was pretty much defined by his powers, doesn't see the harm in it because he's come to resent how he was treated - unable to use his powers, he's dying a slow death.
Helen does, but she goes too far the opposite way; she seems as if she'd be just as happy to never use her gifts again except in small mundane ways.
The truth, as it usually does, lies in the middle: Dash
should use his powers
but in socially acceptable ways - such as bashing rampaging mole men. Helen is shown that she can't deny who she is and that hiding her abilities as as bad as misusing them; she almost causes the deaths of her children because she's not let them use their powers.
Robert is shocked out of his resentment and learns to be a hero again.
Syndrome's later use of the term is totally ironic and meant to show just how single-minded and self-absorbed he really is. He thinks he'll be getting rid of superheroes by bringing everyone up to their level, because of his own inadequacy caused by his total tunnel vision. He can't see that he himself was special even a a child, just that he wasn't special in a flashy manner like Mr Incredible. Everything he's worked for has been a lie.