I've written some articles on this topic. You can't argue with a conservative, because they don't actually mean anything they say.

You can knock down every word and they'll just come up with something else because none of their arguments are fundamental to the discussion. They believe what they believe because they believe it. The words are just whatever seems to work in the moment. Contradiction? No sweat, none of it mattered anyway. Cognitive dissonance? Why? The belief is embedded in faith, no holding of opposing ideas can occur.

Frustrating as hell, but at least knowing that going in can relieve some of the pressure.