In 1958 the Four Pests Campaign called for the elimination of four pests, one of which was the sparrow. Sparrows were accused of consuming grain and as a result were targeted for elimination. A popular sparrow hunting campaign led to the near extinction of the Eurasian tree sparrow in China.
Shortly afterwards locust populations boomed, now missing one of their principle predators. The "smash sparrows campaign" is credited with worsening the Great Chinese Famine, which saw somewhere between 15 and 55 million people die.
The people who smashed sparrows believed it was correct just as surely as we believe anything today.