This topic has left many mouths open and we have to ask: what's the problem, has the cat got its tongue? Here we explain the origin and meaning of this crazy thought.
The expression evokes a strange image, and you are right to think that its origins are just as strange.
Some suggest that ancient kings would punish those who discontented them by cutting off their tongues and feeding them domestic cats. This creepy idea continues in the theory that expression comes from a time of a witch hunt, where fear and hysteria abound. Witches, according to the stories, can steal a person's speech by feeding their familiar or pets.
There is a similar French proverb - 'je jet ma langue au chat' which means 'I'm throwing my tongue at the cat'. However, this is used to mean something like "I have nothing to say" rather than scolding someone for being silent.
Unfortunately, it seems like "the cat got its tongue" as it should have a good origin story, but if so, the description is unfortunately lost. Like children's rhymes or fairy tales, this phrase can be an absurd invention.