Just because they will be 100% unwilling to admit to you that they are actually physically experiencing the feeling of doubt, does not mean it isn't actually happening.
Don't expect them to be honest about what's going on inside them though. They value fighting, never giving up, persistence, dedication, loyalty, strength, power, confidence and security. None of these things makes it more likely for them to admit to you when something they disagree with might sound reasonable.
It's a defense mechanism. Can't just give it permission to function though.
You do have to back off before you actually infuriate them though, as the emotion of anger will strengthen the defense mechanisms dramatically. Better to walk away having peacefully left some food for thought. You can't convince them though, being so readily convinced would itself be unacceptable to them, just on principle.