Aesop may not have existed
The tradition says he was an enslaved man in ancient Greece in the 500s BC, famously ugly, freed for his cleverness, and eventually thrown off a cliff by the people of Delphi. Herodotus mentions him a century later and Aristophanes jokes about him, so the Greeks believed in him. Nobody has anything written by him.
Historians generally treat AESOP as a name that collected stories rather than a man who wrote them — the way a joke you hear today might be attributed to a famous comedian who never told it. Fables already existed in Mesopotamia a thousand years earlier. What the name provided was an author-shaped place to file them, which made them easier to remember and to teach.
The morals were added later, and often badly
The one-line lesson printed at the end of each FABLE is usually not part of the original. Later editors and schoolmasters attached them, and they frequently flatten the story or miss its point. A tale can carry two or three readings; a MORAL nails it to one.
The FOX and the GRAPES is the clearest case. The fox cannot reach the fruit and declares it was probably sour anyway, which is a piece of psychology so exact that it named a real human behaviour — sour grapes. The printed lesson usually reduces this to something about despising what you cannot have, which is true but much less interesting than the observation that people quietly rewrite their own wants to avoid feeling the loss.
Why the characters are animals
Putting a criticism in an animal's mouth is a very old safety device. A story about a greedy LION taking the largest share is a story about a king, and everybody listening knows it, but nothing has technically been said. For someone with no power addressing people who have it, the fable is a way to make a point and survive the evening.
Animals also strip a story to its bones. A WOLF is dangerous, an ANT is industrious, a FOX is clever, and nobody needs a description or a backstory — the audience arrives already knowing. That is why fables are so short. The entire tale of the boy and the WOLF, or the SHEPHERD who cried once too often, fits in a paragraph, and children remember it for life.
The ones everybody knows
The TORTOISE and the HARE, in which STEADY beats fast because the fast one stops for a nap. The LION and the MOUSE, where a small creature spared earlier gnaws through a net later. The CROW with the CHEESE, flattered into opening her beak to sing. The ANT storing food while the grasshopper fiddles. The goose that laid the GOLDEN eggs, killed by an owner who wanted all of them at once.
The vocabulary around them is its own lesson: GREEDY, PROUD, BOASTFUL, CLEVER, WISE. Between three and five centuries of English schooling used these as the standard text for both reading and behaviour, so a good many survive as everyday phrases rather than as stories anybody has actually read.