In a complex system each hierarchical level has novel and irreducible properties. This has far-reaching consequences for managers of complex systems, like you and me. It means that those who know all about one level of a hierarchical system may be unqualified to deal with lower or higher levels in that same system, because those other levels require different kinds of knowledge.
A molecular biologist may be unqualified as a gardener, because understanding how biology works on the level of eukaryotic cells, genes, and RNA, does not imply an understanding of how to tend a garden; while a gardener need not know a thing about chromosomes and genomes to do a good job at gardening. Similarly, the CEO of an organization needs to know a lot about managing businesses, but he could be a complete no-no when it comes to communication, coaching, and other people management skills. (I’m sure plenty of readers can acknowledge first-hand experience with such circumstances.)
Managing organizations requires other kinds of knowledge and experience than managing people, though some knowledge of the underlying levels might be useful. Joel Spolsky proposed The Law of Leaky Abstractions as an explanation of how parts in a system can manifest themselves in counter-intuitive ways in the higher levels, which are supposed to abstract away the lower-level implementation details. Higher-level programming layers that suffer from events in their underlying implementations are considered leaky. Obscure error messages presented to users are another common effect of leaky abstractions in software.
We can see similar problems in other complex systems. My conscious mind occasionally suffers from black-outs, déjà-vu’s, forgetfulness, random memories, and other weird effects, that can only be explained as lower-level irregularities in my neural network leaking through to the higher level that I call my mind. But I don’t have to analyze my neural pathways to put my consciousness to good use, although it is nice to learn from neurologists that the embarrassing quirks in my mind are actually quite common. Likewise, you don’t need to fully understand assembly programming in order to write good higher-level programs, though some lower-level knowledge could make your life easier at times. With management it is the same. One doesn’t need to be a good people manager in order to manage an organization. But some people skills could come in handy, in case things get leaky.