Cladism rests on the idea that we can model the origin of life as a single tree of life. Unfortunately, this model is inconsistent, meaning that it in practice can’t find any kind of things for the model. The problem is that no kind of thing can have a single origin, because it would conflate the concept “kind” of thing with the concept “thing” of a kind. This idea (ie, that kind of thing can equal thing of a kind) is actually a conflation of conceptualization (ie, conceptualization backwards). Unfortunately, we thus can’t reverse conceptualization, because it is inconsistent. We can conceptualize, but we can’t deconceptualize. The route back to preconceptualization is closed.
The problem with cladism is thus that it conflates concepts. This problem is difficult to understand, meaning that many people lack ability to understand it, and thus that many people strive to achieve the goal although it is impossible to reach (thus called cladists). How we shall solve this problem (ie, inability to understand complicated relations) do I not know. I do know, however, that this inability to understand also is the fundament for racism. So, if you can solve it, then I know that you can immunize humanity against racism.
The fundamental problem with cladism, as well as racism in a broader sense, is that it conflates thing with kind, which is inconsistent. Cladism is actually a descendant of nazism.