Why 250 is a rude word in Chinese?
Since it's purely colloquial, there are several possible origins exist.
One source claims that it comes from Paijiu (a gambling game). there are 二板 (four) and 幺五 (six, one plus five). They're the weakest combination in this game. Therefore, 二板五 was invented to call people who accomplish nothing. 二百五 (250) pronounces similarly to 二板五.
Another source says 二百五 comes from literatures in early 20th Century. In Bizarre Happenings Eyewitnessed over Two Decades by Wu Jianren, there is: "...(He) bought a tongzhi(official) with 250 (silver liang), and wanders everyday in the world. " In 1913, a short film (《二百五白相城隍庙》, Fools in Shanghai) depicted a peasant who was in his first visit to Shanghai. He didn't know the etiquettes in cities and made many troubles. Since he was called 二百五, it soon became a popular word indicating stupid people.