It is hard to find an analogy for the classic family tree diagram. It is organic like a real tree growing outside my window, but this analogy is faulty because the representation is an artificial construct. The use of the term "family tree" reflects more of the structure than the reality of the relationships. The tree "trunk," in the case of a family tree, is usually the living member or representative of the family. The "branches" and the "leaves" are the ancestors. Actually, the trunk should be the ancestors. Descendancy charts are a more accurate representation of the family structure than a pedigree chart in the form of a tree. For this reason, fan charts are even less representative of family relationships. Fan charts obscure nearly all of the family structure to show linear or direct-line relationships. They live in a fantasy land of simplicity, like a child's drawing of a tree.
What would an accurate, scale model of a family look like? I think that part of the problem with understanding familial relationships is the predominance of simplistic, 2 dimensional models of the family structure with its focus on choosing only one line at each node in the structure. For example, borrowing from my linguistic background, we are acculturated by our language, while at the same time our culture shapes and determines the structure of our language in a complex feedback system. If I were to attempt to model a language system (which I did for one language), I would soon discover that the model was affected by the passage of time and that however detailed my analysis, the model would always be a two dimensional representation of a multi-dimensional structure. Likewise, trying to diagram a family turns out to be two dimensional and very selective.
In family history, we focus on a specific type of relationship.
Family history is limited, not only by the availability of records, but also by our conceptualization of the types of relationships that exist. When we become fixated on the simplistic fan chart type family representation, we lose the perspective necessary to visualize the complexity of our family. We spend our time gathering names and dates, rather than addressing the real issues of how, why and where our family became what it is in the present time. In all this, we need to look well beyond the visual representations and realize that the diagrams do not represent our family, but are merely a convenient way of recording some, very selective aspects of our family structure.