Why a paternal family tree is NOT an example of nested hierarchy
With a paternal family tree the sets are determined by ONE AND ONLY ONE criterion- "who's your daddy?"
Hierarchical levels: levels are populated by entities whose properties characterize the level in question.
Note the word "properties".
Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below.
Note the words "set of definitions"
The ordering of levels: there are several criteria whereby other levels reside above lower levels.
Note the words "several criteria".