This phrase is not literal; it's used to describe a situation where someone does something that causes a big reaction. Bringing up politics at dinner really set the cat among the pigeons.
Pro Tip 2/3
Expect Surprise
The phrase suggests that the outcome will be unexpected and probably lead to an argument or shock. Her resignation set the cat among the pigeons at the office.
Pro Tip 3/3
Informal Speech
It's used in casual conversation or writing, and might not be suitable for very formal contexts. When Joe spilled the secret, he really put the cat among the pigeons!