As I understand it, his principle complaint is that analytical thinking has become the default mechanism for decision making. For example, if we were to have a discussion on whether people should live in cities or suburbs/rural areas, some people would immediately go to quantities and metrics. Maybe questions about carbon footprints or the cost of transportation or the ability to distribute food. In fact, given the demographic of HN, the vast majority here would probably think that was the correct approach. McGilchrist argues that is the result of indoctrination.
As a counter example, consider yourself feeling hungry and looking in the fridge to decide what to eat. You are unlikely to make that decision primarily based on some kind of analytical process involving calories or costs. You might take those into account (e.g. by avoiding eating cake for breakfast or something) but you would also use your intuition and preference. The same is true when you choose where to vacation, or what music to listen to, or who to marry.
Yet applying the same kind of preference to most other societal decisions is frowned upon these days. We are taught to think critically, to follow the data, to use logic as our primary means. We are trained to silence the non-analytic parts of our decision making process as if allowing them to influence our decisions is almost evil. We are taught to be objective and to break down complex questions into smaller pieces that we can quantify.
This leads to a mismatch between the kind of decision making process that is natural in most areas of life and the decision making processes we champion in modern education and policy making. If you are to believe him, half of our brain is dedicated to an intuitive decision making process - so we are advocating for throwing out half of our wisdom. In his view, if an entire half of our brain is dedicated to that kind of reasoning then we should consider that it has sufficient usefulness that we ought not to completely ignore it or work so hard to suppress it.
Again, I'm poorly steel-manning his position and I don't entirely agree with him. But there is something to be said about his position and its effects. It is hard not to see the general trend to use science to answer all questions, even those that you point out ought to remain free from its dominance.
