How did the phrase "the cat's out of the bag" come up?

Answer 1

because street vendors selling pigs in a bag a long time ago would sometimes scam customers by placing stray cats in the bag. When people would check, they would let the "cat out of the bag", ie expose a secret.

Answer 2

The generally accepted origin of this idiom is middle English:

n medieval England, piglets were sold in the open marketplace. The seller usually kept the pig in a bag, so it would be easier for the buyer to take it home. But shady sellers often tried to trick their buyers by putting a large cat in the bag. If a shrewd shopper looked in the bag - then the cat was literally out of the bag.

Answer 3

TruthHurts is correct. This is also the origin of "buying a pig in a poke". People who paid for the "pig" without checking the sack (or "poke") first were said to have bought a pig in a poke.