There appear to be basically only three reasons for the long persistence of an intellectual controversy.
The first is that the difference between the two sides is one of values and not one of demonstrable fact. If, for example, I think marzipan tastes best and you would say the same about chocolate, then there is simply no rational way to resolve our difference. The same is true for many controversies in politics, especially those that have to do with the more or less equal distribution of money and other resources, although perhaps not as many as one would think; there are many cases where at least one side builds its case on demonstrable falsehoods or on an intellectual framework that contains internal contradictions.
The second is that the two sides are continually talking past each other. Either they do not realize that the other side isn't actually saying what they think it is saying and thus attack a straw man of the other side's position, or some relevant terms are undefined or ill-defined. I believe that the continually resurfacing discussion about free will in the atheist blogosphere is one such issue: the participants virtually all agree on the wrongness of Cartesian dualism, they virtually all agree on some form of determinism (plus perhaps randomness bubbling up from quantum or whatnot, but definitely a complete absence of libertarian or supernatural free will), and they appear to all agree on the emphasis on rehabilitation and prevention in dealing with crime, as opposed to revenge. The entire controversy revolves around whether, all that being agreed on, the word "free will" can still be used in a compatibilist sense: does the word still have a use given determinism? In other words, it is an entirely semantic issue, only some people don't grasp that because they are using different definitions of the term "free will".
Finally, the third possible reason why a controversy never ends is because at least one of the sides is not operating in good faith, does not listen to counter-arguments, is overly prone to confirmation bias, and exhibits willful ignorance. Note that for a long-lasting controversy it cannot merely be honest, innocent ignorance because that would at some point be cleared up, and then the controversy would by definition not be long-lasting. A good example is creationism, where the following has been observed: a creationist argues that evolution is demonstrably wrong because nobody has seen a crocodile give birth to a duck; somebody carefully explains that that is a caricature of evolutionary theory, expounds on the gradual changes in allele frequencies and the long times involved in such a process, etc; and half a year later the very same creationist is again seen arguing that evolution is demonstrably wrong because nobody has seen a crocodile give birth to a duck.
There are of course two stages here: at first one can charitably assume that the creationist is innocently ignorant, although they should perhaps not have entered the discussion in the first place before making an effort at understanding what they are arguing against. But after it has carefully been explained to them why their argument did not make any sense whatsoever, we must drop the charitable assumption of innocent ignorance and must assume that they do not want to listen to what the other side has to say, that they simply do not want to understand the topic at hand, in other words that they are willfully ignorant of it.
I am thinking about this because I recently had to mentally move some "evolutionary" systematists from the potentially innocently ignorant folder into the willfully ignorant folder. Using creationism as an example might appear unnecessarily inflammatory in this context, but the situation is quite the same (and an example from another area such as economics would have been too obscure). Yes, some might argue that the preference for this or that approach to classification is ultimately a question of personal taste akin to marzipan vs chocolate, but even if we grant that - and I don't because systematics should be a science - there would still be valid arguments and demonstrably nonsensical arguments for one of those approaches, and somebody arguing in good faith would not continue to use a nonsensical argument once they know that it is nonsensical. Also, to paraphrase what I recently read elsewhere, the continual use of bad arguments by one side is indirect evidence that their position is not all that defensible.
So in this case I previously charitably assumed that the colleagues in question were honestly ignorant when they published papers promoting the acceptance of paraphyletic taxa and those papers made it abundantly clear that they did not understand (1) what a synapomorphy is, (2) essentially any of the relevant terminology, including even terms like "grade" or "sister group", (3) how parsimony analysis works, (4) that there is a difference between tokogenetic and phylogenetic structures, and (5) that phylogenetic language and phylogenetic systematics only ever apply to the latter, or in other words basically anything they simply need to understand before being qualified to participate in a professional discussion on the merits of phylogenetic systematics.
Don't get me wrong: everybody can have an opinion, but it is another thing to publish scientific papers on a topic without understanding even the very basics of it. Privately I have an opinion on economic policy and I may voice it among family, friends and colleagues, but I would not dream of submitting papers to The American Economic Review. But I digress; the important thing is that until recently I could assume that the "evolutionary" systematists in question simply did not do their homework and honestly believed to have found flaws in the school of systematics that they are campaigning against.
Now, however, I know for a fact that these specific colleagues have read refutations of several utterly fallacious and misguided arguments that they have used before, and they still continue to use them without so much as a blink. They still argue that long branches are a good criterion for the recognition of paraphyletic taxa after they have demonstrably read a clear explanation of why that doesn't work (gradual nature of evolutionary change, intermediate fossils breaking those long branches, lack of an objective and universal quantitative cut-off for "long enough", etc). They still claim that phylogenetic systematics "ignores" evolutionary divergence in lineages after they have demonstrably read an explanation of how information on divergence is found in lists of synapomorphies and how the very recognition of a nested taxon in phylogenetic systematics is necessarily based on the observation that it has diverged from the other members of the containing clade. And they still base their promotion of paraphyletic taxa on circular reasoning after they have demonstrably read a paper pointing out the fallacious nature of the relevant arguments. Part of the problem may be that they appear to also be ignorant about what the word fallacy means - they seem to believe it means "something somebody disagrees with" - and thus presumably ignorant about why it would be problematic to use fallacious reasoning.
Obviously I am not expecting people to quickly change their mind about the paraphyly issue as a whole merely because they have seen some of their arguments blown out of the water, just like I would not expect a creationist to stop being a creationist merely because it has been shown that evolutionary biologists do not actually believe that ducks evolved by a crocodile giving birth to a fully formed duck. Also, no matter how convinced that my own position is the correct one, I should nevertheless still entertain the possibility that proponents of paraphyletic taxa might ultimately be right, perhaps because of some argument that I have not yet fully considered.
But at a minimum I would expect them to make some attempt at at least somehow dealing with very clear refutations of their individual arguments. They could try to show that their arguments are actually not wrong (although admittedly in the case of their straw man version of phylogenetic systematics that would be quite difficult) or they could switch tactics and use another line of argument. But instead they blithely repeat the same talking points, never even so much as acknowledging that those might possibly just have been addressed in some way or another.
So they now knowingly continue to mischaracterize the school of systematics that they are attacking, and they knowingly repeat arguments that are demonstrably fallacious and/or based on faulty assumptions, and that is seriously not a question of values or taste. At some point, they have to dimly register that the other side always replies "actually, no, that's not how it works" when they describe how phylogenetic systematics supposedly operates. At some point, they have to realize that an argument does not become less unfounded merely by repeating it over and over again while going "lalala I can't hear you" whenever somebody answers.
And that is where the charitable assumption must be dropped. We all should, ourselves, whether it is a topic of professional relevance or only of private interest to us, whether it is about science, religion, politics, economics or whatever, listen to opposing arguments, evaluate them honestly, put our own ideas to the test, and assume until the opposite is proven that others are doing the same. But at some point one has to observe the behavior of the other side in a controversy and decide whether they can still be assumed to argue in good faith. If they are visibly ignoring even the clearest refutation of one of their arguments, if they appear continually disinterested in learning about and understanding even so much as the basics of what they reject, then one has to conclude that a rational discussion is not possible.
That does not mean one should stop arguing, of course. It is still important to try to convince the people sitting on the fence. But that realization has consequences for the way one has to argue as well as for
what degree of intellectual honesty one might potentially expect from
the other side.