Necessary Knowledge

Apparently to deny an analytic statement is to deny or self-contradict an apriori statement, and that woul be an act of lunacy and absurdity.

Is there ever a case where a contradictory or self-contradictory statement about and denying the truth of an analytical proposition, could be true, sensible and meaningful? Perhaps extreme fallibilists would make this claim, and epistemological moderates too, but, in the main, we cannot contradict an analyitic statement or true synthetic statement without talking nonsense, a lie.