Where does The Crow and the Fox come from?
From a long way back. Aesop already tells of a crow holding a piece of meat and losing it for wanting to sing; the Latin fabulist Phaedrus takes it up. La Fontaine makes it the second fable of his first book, right after La Cigale et la Fourmi. He changes neither the bird nor the trick: he changes the tone, and replaces the meat with a cheese.
One word often stops readers: the Phoenix. It is the unique bird of legend, reborn from its ashes, of which only one exists in the world. Telling the crow he is "le Phénix des hôtes de ces bois", the Phoenix of all the dwellers of these woods, is telling him that no bird in the forest is his equal. The fox never flatters by halves.
1762
Rousseau, Emile, Book II
the fable read line by line
Nearly a century later, Rousseau takes it as an example of what should not be given to children. He dissects it line by line, "Maître! what does that word mean?", and concludes that the pupil will learn the wrong lesson: "children make fun of the crow, but they all grow fond of the fox." Which mostly proves that the fox is irresistible.
Does the fox lie to the crow?
Not quite, and that is the finesse of the text. The fox never says the crow sings well. He says: "si votre ramage se rapporte à votre plumage", if your song matches your plumage. Everything lies in that "if". He sets a condition, lets the crow fulfill it all by himself, and so will have stated nothing false. Effective flattery does not lie: it suggests, and lets the other take care of the rest.