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In one side-story of the series, it was believed that the Diclonii were chosen by God to exterminate the current humanity, and then replace them themselves. When pushed to the brink of no return, a Diclonius would hear a voice in their head, and the voice commands them to kill as many human beings as possible. This could explain most of the killings done by the Diclonii since it's just implanted in their DNA to destroy all humans. There's also the possibility that a Diclonius can become a sadistic individual overtime if said Diclonius were molded by their environment.
As a result of their appearances, Diclonii tend to be heavily discriminated. This is evident in the anime and manga series when a group of bullies bullied Lucy and called her terrible names based around her horns. They also callously slaughter her puppy just to get some emotion out of her. Because of their actions, Lucy grew to hate humanity, and she became a cold, homicidal maniac as a result. However, most of the prejudice towards Diclonii stems from the fact that they could be a threat to humanity. While it doesn't justify most of the government's treatment of these mutated humans, in a way, it is justified, and it was ultimately decided that the Diclonii had to die so that humanity could be safe.
By the time that the manga ended, many young Diclonii were killed along with many humans.