I will write more about other stuff, but as mentioned before, I would like to write this all out for once in case I ever want to refer to it. Warning: long and technical, although perhaps even a non-biologist may find the last part amusing.
As indicated in my introductory post on the topic, Phylogenetic Systematics (PS) is today the dominant paradigm in biological classification. Perusing the pages of the major journals of systematic botany, such as Taxon, the Botanical Journal of the Linnaean Society, Plant Systematics and Evolution or appropriately named Systematic Botany, we will always find numerous publications either suggesting that a plant group be recircumscribed to make it monophyletic or expressing satisfaction at having confirmed the monophyly of a group in its traditional circumscription. And the latter happens more often than many people assume, by the way.
Still, a vocal minority of botanists remains opposed to the requirement to accept only monophyletic supra-specific groups. This might appear surprising: should scientists not be able to figure out amongst themselves what is the best approach and then be reasonable enough to all follow it? Well, most of us think we have done so.
So, what arguments do the remaining opponents of PS advance, and are they any good? Unfortunately, going through all that discussion would take far to long. I have elsewhere published a point by point rebuttal of all arguments I could find in the botanical literature, and I may address individual arguments in more detail here in the future, but in specific posts. For now, let us take a step back, assume a more general perspective, and ask a slightly different question: who are the people who still reject the monophyly criterion, and what motivates them?
The first observation here is that the opposition is surprisingly heterogeneous, both in the issues the individual opponents raise and in the style of argumentation. The following classification is necessarily subjective, and there is clearly overlap between categories two and three as well as between three and four, i.e. one person can belong to two of these.
1. There are end-users of biological classification, for example horticulturalists, gardeners, traders, publishers, and perhaps even some collection or database managers, who are mainly interested in stability and thus get annoyed when botanists change plant names to make groups monophyletic. While other colleagues need a scientifically accurate, natural classification to be able to address biogeographical or evolutionary questions, or to target plants for breeding or drug discovery, the above professions mostly use the classification as a means of communication. In the ideal world of at least some of them, plant names and classifications would never change because that would make their job easier.
On the one hand, that is very understandable: they have a different view of what a classification is good for. On the other hand, it is also remarkably silly. As an Australian colleague recently wittily pointed out at a conference, none of them have problems with changes that were enacted before they went to university and learned the classification that was accepted then; and logically, if stability were really the greatest virtue in classification, we should still be using the systema sexuale of Linnaeus. Put like that, it should be very clear where the problem is. Science is about continually improving our understanding of nature, and thus science is fundamentally incompatible with stability. Demanding that classifications and names never change because it is inconvenient is as twee as a cartographer from 1492 complaining about having to put a new continent on their maps, or a physician complaining that the demand for bloodletting has gone down.
It could also be mentioned that botanists changed names and classifications all the time even before the monophyly criterion was introduced - the systema sexuale was scrapped long before 1966.
2. On a strange meta-level, there are biologists who would in principle agree with the monophyly criterion (or don't care about it either way), but who are concerned with offending the previous group or the plant-loving public in general. The idea is that research fields like systematic botany have to struggle for funding and respect anyway, and we are not helping our cause if we are perceived as making spurious and annoying changes all the time.
This second group is not very outspoken, but at the aforementioned recent conference, somebody made this argument in the discussion after a talk on Proteaceae. Another colleague gave what I consider the only reasonable answer: As scientists, we surely would also not lie to the public and tell it that the earth is flat if it wanted to believe that. What we should do is treat everybody as a grown-up and explain very clearly how and why we arrive at our conclusions.
3. The third group is the one that potentially has to be taken most seriously: systematists and taxonomists who make what they consider to be scientific arguments against the monophyly criterion. I include in this group practicing, professional scientists who have repeatedly published opinion papers and letters in peer-reviewed botanical journals to advance their cause. Many of them call themselves "evolutionary systematists" to differentiate their position from phylogenetic systematics.
This small group advances many different arguments, but most of them are based on misunderstandings of the principles of phylogenetic systematics (in particular a failure to appreciate the difference between tokogeny and phylogeny), on fallacious reasoning, or on willful ignorance of the fact that the perceived "evolutionary divergence" of paraphyletic groups from other groups nested within them is an illusion, an artifact of the extinction of intermediate forms which, however, can and do still turn up as transitional fossils.
In fact, there is in my opinion only one person in this group who builds his case on an argument that is (arguably) not constructed from false premises and/or faulty reasoning. Brummitt (2002, 2003) argued that the binominals we use for species - where each species name consists of the name of the genus it belongs to plus a specific epithet, like Homo sapiens - is incompatible with the enforcement of monophyly if we try to classify ancestral species. Imagine we would discover a fossil of the progenitor species of all of life, and we wanted to give it a name. To have a binominal species name, it needs a genus name. Because it is the ancestor of all of life, this ancestral genus would, however, be paraphyletic to all other, descendant genera. Thus we would have to unite all of life into one genus to make it monophyletic.
The thing is, of course, that with extremely rare exceptions we cannot know if any fossil species is truly ancestral to others or merely a side branch close to the real ancestor. For this and other reasons, Brummitt's argument seems a bit far-fetched. And even if we accept it, it merely shows that binominals and the requirement for monophyly are incompatible, but not that we should give up the second of the two. One could also prefer to scrap the binomina (see also: PhyloCode).
4. Finally, the fourth group rejecting phylogenetic systematics are the the ones that invite a comparison with creationists, germ theory denialists and other conspiracy nuts. Their motivation is unclear, especially because they rarely make enough sense to fathom it. In fact one wonders how an issue as mundane as systematic biology can produce such derangement, compared with more obvious candidates like evolution or climate change. But well, perhaps we can take it as an indication that our field is not quite as obscure and irrelevant as some people like to think, if it causes such emotional reactions in these detractors.
Defining characteristics of this group, which of course are not always all present in the same person, are for example the production of long, convoluted screeds denouncing phylogenetic systematics, here usually called cladism; the conviction that they, personally, have developed a new and better approach to classification, but the cladists are just too biased to recognize its superiority; the excessive use of pseudo-philosophical gibberish disconnected from any empirical considerations, claims that the demise of phylogenetic systematics is imminent; and the characterization of its practitioners as radicals, fundamentalists or quasi-religious for promoting an objective, testable methodology (in other words, science). Some of them enjoy the erratic use of all caps or perhaps of different font sizes, formats and colours in the same paragraph, as in one e-mail I received a few months ago.
A perfect example of several of these characteristics in combination can be found at this interesting blog. While terribly concerned about finite vs. infinite classes, objects vs. classes, types, conceptualization, essentialism, universals and suchlike, the author shows little to no interest in developing a mental model of what actually happens in evolution and what that means for our attempts to build a useful and accurate classification of the diversity of life. Just imagine you are a cartographer, and while you try to place rivers, lakes and mountains on your map, somebody constantly lectures you about how the contours of all the things on your map are in reality fractals, so it is futile to ever represent them on a map, and you haven't properly defined whether this river is, from a philosophical perspective, really a different "object" than its tributaries, and so on and on and on and oh please make it stop, and then he goes and crudely photoshops a famous cartographer's face onto a cartoon, and then onto another one, because the first time it wasn't trashy enough...
Okay, admittedly this is nothing compared to creationists. At least opponents of phylogenetic systematics don't vilify the other side as Nazis, like the creationists who claim that the theory of evolution motivated the Holocaust. Oh, wait. Seems I spoke too soon.
As mentioned above, there is some minor but distressing overlap between this and the third group, and thus similarly opaque gobbledegook sometimes even makes it into professional publications. Minus the crude cartoons and the Nazi-baiting, admittedly.
Brummitt RK, 2002. How to chop up a tree. Taxon 51: 31-41.
Brummitt RK, 2003. Further dogged defense of paraphyletic taxa. Taxon 52: 803-804.