[DanBC]

> Talking out of both sides of your mouth means saying contradictory things,

It's a bit more than that, isn't it? There are elements of dishonesty.

From Cambridge Idiom Dictionary

> be speaking/talking out of both sides of (your) mouth

> American

> to say different things about the same subject when you are with different people in order to always please the people you are with.

> How can we trust any politicians when we know they're speaking out of both sides of their mouths?