The story behind the Chinese word for contradiction is an interesting one. The story goes that an arms trader at a market was touting his spears as the strongest, and able to pierce any armour. While at the same time claiming his shields were also the strongest, and able to withstand any weapon – Until someone questioned what would happen if the trader’s spears were used to attack his shields, highlighting the illogicality of his statements. The result is that the Chinese for “contradiction” is literally “spear shield”.
Though the idiom is 「自相矛盾」, which is a self-contradiction as demonstrated by the arms trader above, you can also simply use 「矛盾」 to say that something is a contradiction.
The following image from CCTV news illustrates this idiom perfectly.
yǒuhài qìtǐ búhuì shānghài huánjìng hé rényuán
Harmful gas won’t harm environment or people
A contradiction in terms if I ever saw one.
Here’s a cartoon on Youtube that tells the story of this idiom: