Difficult Conversations Have Three Basic Aspects
I have been able to observe these three in all strenuous conversations so far.

One of the insights I gained from the book Heikle Gespräche1 (or Cruicial Conversations in English) was that difficult conversations consist of three different aspects, namely the following:
Opinions clash
Emotions are running high
Something is at stake
That opinions clash because the participants in the conversation have different views is an obvious aspect.
That something is at stake (e.g. one’s own identity if one has made a mistake) is also clear.
But the aspect with the emotions was the most interesting for me. Not because it is not also obvious. The facial expression changes, the voice becomes more tense and forceful, the gestures become more aggressive — all this is easily observable.
What is interesting to me is the reason.
In difficult conversations, an old brain structure kicks in, which then leads to this kind of expression: the amygdala.
The amygdala is an almond-sized area in the limbic system. It controls our fight-or-flight response.
The authors write that blood is drawn from the brain and pumped into the muscles, because to fight or run, it is needed more there.
The newer areas of the brain (the neocortex) are thus less active, but the brain stem is. The problem is: the neocortex is responsible for rational thinking.
This was a comprehensible explanation for me why difficult conversations can often be very irrational.
Patterson, K., Switzler, A., Grenny, J., & McMillan, R. (Hrsg.). (2012). Heikle Gespräche: Worauf es ankommt, wenn viel auf dem Spiel steht (2., aktualisierte und erw. Aufl). Linde-Verl.