The theoretical basis for cladistic classification into monophyletic (holophyletic) ranked taxa is fatally flawed and is promoting bad taxonomy. Biological classification that takes account of evolutionary history may be based on two main factors—lines of descent and extent of divergence represented by morphological and other characters. In taxonomy a balance must be found between lines of descent and characters, and insistence on one at the expense of the other will give unacceptable results. Much confusion has arisen in systematics from the failure to appreciate that taxonomy, which groups organisms into ranked taxa (families, genera, etc.), is essentially different from grouping them into clades. These two processes are based on conflicting hierarchies and have different methodologies and functions. For several decades, however, the cladistics movement has adopted lines of descent rather than characters as the sole basis of taxonomy, insisting that only complete clades should be recognized as taxa. But as soon as one imposes ranks on a phylogeny, one must create paraphyletic taxa. These are natural products of evolution, which should be recognized in taxonomy. When ranks are adopted without acceptance of paraphyletic taxa, taxonomic free fall sets in, and every clade sinks into those taxa to which its original ancestor is referable. The clash of hierarchies results in absurdity, extending to sinking the entire plant kingdom into one family and one genus, but this has been strangely overlooked by the cladistic side. Adoption of ranked taxa is incompatible with recognition of only complete clades. Merely because one taxon falls phylogenetically within the clade of another taxon at the same rank does not necessarily mean that it must be included in it taxonomically. New characters will have arisen during evolution, which should be taken into account. A monophyletic (= holophyletic) system recognizing only complete clades is logically possible only if ranks are abandoned, as in the PhyloCode. It may be referred to as a “cladification” and the process producing it as “cladonomy,” which are quite different concepts from a “classification” and “taxonomy.” In a classification we have a hierarchical series of taxa at different ranks, while in a cladification we merely have a hierarchy of clades nesting within successively bigger clades. Cladistic taxonomy is particularly nonsensical in paleobotany, where our Linnaean taxonomic system and our code of nomenclature apply just as they do for extant plants. Cladograms are not classifications, and they need critical taxonomic assessment. The great majority of users of taxonomy are interested in characters and not cladistic theory. A general purpose classification is needed, requiring acceptance of paraphyletic taxa that are defined by characters as well as lines of descent. Examples in the dicot flowering plant families are given in which cladistic principles have imposed excessive insistence on lines of descent at the expense of evolution of characters, producing what many regard as bad taxonomy.