Throwing (also putting and setting) the cat among the pigeons is a British idiom used to describe a disturbance caused by an undesirable person from the perspective of a group.
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Another use of the term is to "cause an enormous fight or flap, usually by revealing a controversial fact or secret", or in other words: to do something suddenly or unexpectedly which leaves the people worried or angry.
History and usage
The phrase originally referred to the disturbance likely to be created by putting a cat inside a dovecote (or dove house). This disturbance is caused by the cat's tendency to hunt and kill the birds, only made easier by their close proximity.
Similarity in other languages and cultures
Whilst being similar to other idioms such as the German-language phrase das fünfte Rad am Wagen (the fifth wheel on the car), in this case there is an element of aggression, and a power differential becomes the key element in the undesirability. The Spanish-language version of the phrase is alborotar a todo el palomar. In Russian, there is a proverb similar in meaning "пустить козла в огород" (let a goat into the garden).
In colonial India, a popular pastime was to put a wild cat in a pen with pigeons. Bets would be made on how many birds the cat would bring down with one paw-swipe. The period of the British colonisation of India may have introduced this concept, and hence the phrase to the English language.
In popular culture
Cat Among the Pigeons (1959) is the title of a detective-fiction novel by English writer Agatha Christie.