"For the Greater Good" was a sort of rallying cry for Grindelwald and his followers during the 1920s through the global wizarding war in the 1940s. Grindelwald's ideology of a world where wizards ruled over subservient Muggles was fostered during his time with Dumbledore in Godric's Hollow.
Because of the tragedy of Dumbledore's sister Ariana, who was left emotionally traumatized from an attack by Muggle boys, Dumbledore became infatuated with Grindelwald and his ideas to topple the International Statute of Wizarding Secrecy. "For the Greater Good" was coined by a Dumbledore as a way to justify the violence that would surely come to meet their goals of wise and gifted wizards and witches taking their "rightful place" above Muggles.
"He's mistrusted by the Ministry; they know he has this dark past in which he flirted with Grindelwald's ideology," Rowling said in a film extra on "Fantastic Beasts: The Crimes of Grindelwald." In "Harry Potter and the Deathly Hallows," Dumbledore tells Harry Potter more about his relationship with Grindelwald, their shared ideology and their obsession with the Deathly Hallows.
"It would all be for the greater good, and any harm done would be repaid a hundredfold in benefits for wizards. Did I know, in my heart of hearts, what Grindelwald was? I think I did, but I closed by eyes," Dumbledore said.
