The story
From toad + eater, said to allude to an old alleged practice among mountebanks, who would hire a boy to eat (or pretend to eat) toads, which many had considered poisonous. The toadeater (or "toady") would pretend to writhe in pain, until the quack gave him some "medicine" and pretended that the boy was cured. Compare toady.
Etymology from Wiktionary, CC BY-SA 4.0.