Using a word "correctly" isn't actually something everyone agrees on, though. As much as certain usages rub me the wrong way, it's hard for me not to fall on the side of descriptivism and that the issue is with my reaction rather than other people; words are all just made up sounds (and written symbols, of course) that we use to communicate, after all, and if enough people use them in a certain way, it doesn't really make sense to me that there would be some inherent meaning that overrides that. Language evolving isn't a new thing, and once a meaning reaches enough mindshare, there's no turning back.
Language changes, sure, but only because people change language. The changes, and lack of them, are always the result of an ongoing negotiation and evolving consensus as to what words should mean and how they should be used.
Sometimes prescriptivism is pretentious nonsense (like hypercorrection), status-seeking bullshit, or bullying masquerading as erudition, but sometimes it's just an explicit contribution to that ongoing negotiation and consensus.
When one of my students submits an essay containing the word 'over-exaggerate,' I correct it, striking out 'over-.' The word appears in dictionaries, so in that sense it's standard, and my correction is wrong, but it is an ugly, stupid word and should never appear in academic writing (and literate college students should know that). In my students' writing, it has increasingly replaced the simpler, better "exaggerate."
It's my responsibility as a teacher to encourage my students to think about the choices they make and the language they use, especially in an academic context, but I'm also hoping to cultivate the habit more broadly of just thinking about their choices, understanding that there are choices, and recognizing that the alternative is to be at the mercy of whatever consensus they're receiving from pop culture.
In most contexts, outside of a classroom, I won't bother with the correction, because it would be obviously unwelcome and inappropriate, but it has its place.
The line between descriptivism and prescriptivism is also very porous. Usage largely determines correctness, so unless you want to throw correctness completely out the window, there are going to be gray areas where either usage isn't widely agreed or where it really is necessary to correct language that falls afoul of standard usage regardless of whether the incorrect use will eventually be deemed correct.
Anyhow, 'disinterest''s disputed sense fills a hole in the language: 'uninterested' is a word; 'uninterest' isn't. People have solved the problem by collapsing the two words into one -- so that 'disinterest' and 'uninterest' are synonyms -- and throwing away the meaning of disinterest they use less often.
If I accept this, English loses some of its complexity and color. I don't want that.
Moreover, key texts and concepts become harder to appreciate if its sense corrupts this way. What do people think "disinterested justice" is if they don't know the meaning of the word? This kind of literacy is, I think, a basic building block of critical thinking. One can't think effectively, particularly in a social (political) setting, if one can't use words effectively.
When grading papers from students, it's reasonable to correct their usage. I'm probably reacting to all of this because the impetus of this discussion was someone rehashing a complaint that I suspect most of us have already heard about a word no longer only having a meaning that's so uncommon that it's not unreasonable for it to no longer have a single word for it stemming from its usage in an article by an author who likely won't ever read these comments.
I'm also not super convinced that people won't be able to understand concepts like "disinterested justice" because there's plenty of other terminology for that like "impartial" that are arguably much more common; I'm honestly not sure I've ever heard the term "disinterested justice" before now. I can at least see the value of that viewpoint being expressed even if I don't agree with it though, so in retrospect I should have responded before directly to the comment about "decimate" rather than replying to your response.
The short answer is that disinterested means unbiased, having no conflicts of interest, impartial. So a judge in a court should be disinterested, but not uninterested.
Using "disinterested" to mean "uninterested" has become more common over the past few decades, rather than using it in the older sense of "having no stake in the outcome, having no bias or partiality with respect to a conflict."
An example would be saying that someone was "disinterested" in what was happening on TV, or in music that was playing.