When Willi Hennig (“the father of cladistics”) concluded that “only monophyletic groups appear to be natural groups”, he really turned sense and nonsense up-side-down. The statement is extremely difficult to question since it uses the ambiguous concept “monophyletic” unambiguously, and appeals to realism in a sense of appearing to be trivially true. So, what’s the problem with it?
Well, the problem is that it conflates the concept “class” with the concept “thing” in the concept “species”, when we (humans) actually conceptualize reality by distinguishing things and classes by distinguishing classes of things (and that the concept “class” thus actually is orthogonal to the concept “thing” by definition), because it thereby actually conflates conceptualization itself.
This problem means that Hennig’s approach (then called racism, and today called cladistics, but correctly called realism) is fundamentally paradoxically contradictory, because conceptualization is fundamentally paradoxically contradictory, as Bertrand Russell demonstrated with Russell’s paradox.
A simpler explanation is that Hennig’s approach is paradoxically contradictory because it conflates what it distinguishes. (It is contradictory to assert two contradictory opinions simultaneously, but it is moreover paradoxically contradictory to conflate what one distinguishes).
Hennig thus turned a paradoxically contradictory nonsense (ie, realism) into an apparently trivial sense (in the service of Nazism), which, surprisingly, also dominates biological systematics today. There are thus still the same ugly fishes of race biology lurking in the murky waters of biological systematics today as there was before the racial beginning of the 20-th century.