To have a difference in opinion and respect each other for it, is golden. This is an ethic worth living by in the promotion of an environment that promotes candid discourse.
However, there are those instances when actors set out to intentionally break down discussion by being unreasonable. What is worse is if it is done with a certain degree of intelligence and calculation. How does one deal with. such towering negativity?
In my humble practice, I spent many years succumbing to disbelief and even disgust at such machinations and it filled my cup with multiple storms of anger. Later I realized that it was possible that the crafter had already figured out what my first reaction would be to his/her behavior and saw it as an opportunity to execute.
In silence, as the unreasonable conduct is being meted, see it from afar and kill it with kindness. Use kind words and speak slowly enough for clarity of thought and objectivity. Emotion should be safely tucked away or deferred to a safe place that does not breed disadvantage. Eye contact should be to show that your kind words should not be mistaken for weakness. Confident gestures that welcome progress should dominate your demeanor.
Tell me how it goes when you try it!