The fundamental problem for the approach in biological systematics called “cladistics” is the fact that a dichotomously branching process can’t be consistently illustrated with a dichotomously branching graph, because a “line” in the process (ie, a thing) corresponds to a node (ie, a branching point) in the graph. This fact did also “the father of cladistics”, Willi Hennig, note in his Figure 15 although he obviously didn’t understand the significance of it.
This fact does, however, mean that the properties of the things of any such process can’t be consistently mapped on any such graph, but instad are bound to lead into a paradoxical contradiction somewhere in every such graph. The graph simply conflates the process with its patterns. This fact is actually in essence “Russell’s paradox”.
This fact means that it does not matter whether evolution IS a dichotomously branching process or not, because it anyway can’t be consistently described as one. Cladistics’ claim that the process of evolution can be consistently decribed with a dichotomously branching graph is thus simply wrong. Instead, this claim actually waves farewell to rationality in favor for irrationality.