Powereds are superhumans who have sporadic, limited, or no control over their power. This is due to some unknown factor, not a lack of discipline or training.
In this world, there are 3 "classes", you've got Powereds, Humans and Supers. Powereds and Supers are humans with abilities, but Powereds cannot control their abilities. Because of this, they are pitied, considered a nuisance (accidentally setting a business on fire because they sneezed; or blowing up a television due to uncontrolled power of good or bad luck) and are considered "3rd class". The world has become somewhat "racist" against Powereds, making them the butt of jokes, thinking of them as lesser people, and supers even downright hate them; supers are even more susceptible to this line of thinking. There is a theory it's because supers know they could have been a powered if not for some small genetic change, they are/were very close to being a powered and that scares them, so they lash out at Powereds.
The "cure" for the malfunction that Powereds have is one of the most sought after scientific discoveries in the world, and has apparently been found by one private organization, which resulted in the successful creation of the 5 Melbrook students. Powereds are generally viewed as pitiable and potentially dangerous by both humans and Supers alike. There is one theory that Powereds are that way because they're too powerful, and their bodies or minds couldn't take it or control it, and thus they're powered. The 5 known cases of Powereds becoming Supers does seem to support that theory.
However there is another theory that humans are already upset about becoming "#2" on the evolutionary scale, but they can tell themselves that at least they're not Powereds sitting at #3. If Powereds were to be cured, it could potentially mean Powereds would become #1, Supers would become #2 and Humans would become #3. Considering that Supers are even more "racist" against Powereds than humans, there's a high probability they wouldn't take kindly to being bumped down by Powereds, and humans wouldn't take too kindly to becoming #3, at the bottom.