Saying something without conviction might be called a lie, or you could be accused of “talking through your hat.”
Around 1850, an Englishman refused to kneel before sitting in a church pew, a serious breach of religious etiquette.
Instead, he whispered a prayer while covering his mouth with his hat before sitting down.
This shocked the other worshippers, and although many copied him, “Talking through your hat” took on the meaning of false and irreverent.