I think that Illumi's family put a needle in his head years ago but that needle got shoved in farther than intended and it fucked him up. They deadass lobotomized Illumi.
I imagine that Killua was an infant. Illumi was about 11-12 and Milluki was 5-4 and Illumi was starting to get rebellious and was actively trying to get him and Milluka and possibly baby Killua out of there, when he realized that he was living in a house of horrors.
He went to go see his baby brother and tend to him because he heard him crying but instead saw his parents electrocuting him and felt a sense of protectiveness rush over him and ran to save him but was held back
So he made a plan to escape with Milluki and Killua but Silva caught wind of this and stopped him.
So what was Illumi's punishment ? Silva thought needle implant that would "cure his rebellious tendencies" and make him focus on assassination. It was a fairly old technique that he didn't even master yet, but he couldn't have Illumi taking his heir away, so he tried it anyways.
Illumi was probably strong as a kid, so his fighting caused problems and with Silva trying to stop his squirming, accidentally ended up shoving the needle into his brain at full strength, way too deep, in a weird angle.
Illumi's screaming stopped. His fighting stopped. And he went limp. Silva thought he had killed the boy at first, but after a few days of being passed out, Illumi woke up as an entirely different person.
His family didn't bother removing the needle, because even though it fucked him up personality wise, it made him a lot more obedient. Illumi doesn't even remember the needle getting put in his head or what he was like before that, all he knows is that he woke up one day fascinated by them and incorporated then into his assasination style. Silva even tought him how to implant them in people's brains after he had finally perfected the technique.
All Milluki knew when Illumi woke up was that his Illu-Nii didn't want to play anymore and didn't even notice him whenever he tried to get his attention and Killua ended up losing a brother who truly wanted to protect him and gained an emotionless puppet of a brother who thought he was "protecting" him when in reality, he was hurting him.