Triune brain is oversimplification that works for oversimplified cases. Neocortex handles advanced cognition. Limbic brain controls social and nurturing behaviours, mutual reciprocity, and the reptilian brain refers to those brain structures related to territoriality, ritual behaviour and other reptile behaviours.
Reptilian brain is a popular concept found in many books. It is an oversimplification found in triune brain concept.
Oversimplification is usually useless apart from a basic introduction to a topic. When combined with other simplified models, it can sometimes help create a mental model for us to follow. It is valid for presenting projects and the basic construction of narration.
When we work on a complex topic, we use neocortex, the brain parts that handle more advanced cognitive processes. We assume that people will use the same part of the brain to receive our presentation about the complex topic. That is not true.
For a complex topic to reach advance cognition, our communication must first pass past reptilian brain, primitive parts of our brain that sense danger and control basic behaviours.
Next, there is a limbic brain that handles social behaviours.
If our presentation is only about facts, raw data, long, uninteresting and complicated, the reptilian part will shut people off. If we do not refer to why people should care about us and our project, the limbic systems will cut us off. (See, with a grain of salt, more examples in Pitch Anything by Oren Klaff).
It is important to remember that the path to high hills leads through valleys and woods. We cannot drop our high mountain thinking directly on to another high hill – we must walk the whole path.
To reach System 2, we must first go through System 1 (Thinking fast and slow, Daniel Kahneman).