I'd like to tell you a story I heard from my old man. My father worked in the University of Wales in the 1990s, practicing medicine as well as committing to biomedical research (psychopharmacology of addiction). Every week, my father and his colleagues would get together and formally discuss things pertaining to medicine. One of those meetings included Dr. Robert Newcombe, professor of biostatistics. In my father's recollection, he began criticizing the methodologies of many reputable, peer-reviewed medical studies. He tore them apart, one after the other. My father left that room in an existential crisis, wondering how much of what he taught was bogus. He often quotes Sackett: "Half of what you'll learn in medical school will be shown to be either dead wrong; the trouble is that nobody can tell you which half." Why do I say this? Well...
It's because I wanted to illustrate that even the stereotypically sciency sciences have the ability to struggle with imprecision, as well as the importance of methodology above object of study. While the natural and formal sciences have somewhat of a general methodological consensus, the social sciences differ strongly from one academic to another; some academics do work closer to biology (collecting data, quantifying it statistically, running simulations, et cetera) and others do work closer to literary criticism (reading texts, considering possibilities for relations to societal practices and traditions). The latter are maligned as "not scientists" (which, while arguably true, isn't necessarily a bad thing), and the former are maligned as having "science envy" (as though using statistical analyses on textual data is somehow wrong).
Naturally, the social sciences coalesced far more recently as an independent discipline in comparison to, say, physics, and this nascency could be the reason for methodological disagreement (after all, science began with simple observation). In my opinion, while that idea holds weight, there's something larger at hand: the focus on sciences in terms of the object of study, instead of methodology. Different methodologies answer different questions. If you're interested in the potential religious themes in the Canterbury Tales, a more critical approach is what you'd regularly go for. If you're interested in the types of words loaned from French and Italian in comparison to Old English, then a statistical approach would offer some answers. A statement such as "52% of words in the Oxford English dictionary come from Latin" is something that can be empirically shown. A statement such as "Western fascination with the East is born out of a will to subjugate the Other" cannot be, at least in the same sense; it may be argued, however, in accordance with a framework (in this case, post-structuralism).
One argument I often hear levied against the digital humanities, and more generally highly empirical research studies within the social sciences and humanities is the idea that humans are too complex and numerous to model using statistics. To that, I say: that is precisely the point of statistics. There are similarly complex models in biology (DNA analysis and prediction, microbe activity, the structure of the human brain) that use statistics because it's difficult or even impossible to know the state of every constituent of a system under study. Statistics is often portrayed from the outside as certain, despite the fact it is anything but certain, rather it is the manner in which something can be known to be uncertain and in what terms.
It seems, at least to me, as though this split is born out of the differing cultures of STEM and liberal arts, where the social sciences (and especially digital humanities) are caught in the middle, not quite one, not quite the other. One argument I hear consistently levied at the digital humanities has nothing to do with the methodology at hand, but the fact/idea that digital humanities research is prioritized for grants and is thus considered better or more proper by investors. With the advent of AI and large language models fed on textual data, the same kinds studied qualitatively and interpretively and the AI mega-summer we've experienced in the 2020s, some humanities students and scholars feel left out.
To be clear, this isn't to say that it's jealousy or elitism that makes one side hate the other, but rather that the vision of a conflict between these two methods is, in the least in part, inspired by a minimal amount (or lack) of accord between scholars who focus on different questions with different manners in which they could be answered, and that accord is only amplified by the different kinds of institutions in which they're housed. The truth is, "Did a hurricane happen here?" and "How did it feel when your house got destroyed by it?" are two questions about a hurricane, but two different ones; the latter is individual and subjective, while the former can be corroborated by others.