Although Sherlock's reasoning was very complete and reasonable, only Aiwass knew that Sherlock's answer had definitely been wrong.
Because he was missing an important piece of intelligence, but Aiwass especially couldn't reveal this information to Sherlock.
Sherlock, following the clue from Aiwass's grandfather, found the Noble Red Society. Coupled with the Pelican Bar, Giant Remnants, and the smuggling case, he logically concluded that Aiwass's parents had been killed by the Noble Red Society.
This deduction was completely logical.
However, during the Dream Realm ceremony, Aiwass, as the Aberrant Limb Demon, interrogated the Cursing Sorcerer "Aziz Ben Abdul" and learned from him that he served Professor Moriarty. He was the true master of the Hook Demon, the one who killed the entire Alexander Family.
But he was not a demon sorcerer from the Noble Red Society.
He wasn't even an Avalonian, nor did he have any connection to the Giants or Star Antimony people... he was Parthian.