I did a degree in Linguistics. I wouldn't say it makes me an expert on "grammatical correctness" (nor an expert in much - insert condemnation of the lowly BA here) because as a social science it at least pretends to only describe what occurs, not say what should occur.
The argument put forward in Linguistics is that if grammar is to be useful, it must just be what the majority of native speakers within the same region consider acceptable use. Same with how dictionaries should be, really. Recording language as it is used.
There are many other ways to argue for grammatical correctness, eg. referring back to the source languages of words, the history of usage within the language in question, etc. but (as with music criticism) you're just arbitrarily setting up the criteria by which you assess what is valid and what is not. If someone else disagrees with the basic criteria then all your arguments fall down.
So here's some ways to dismantle the argument that "burglarize" is a more correct verb form than "burgle" because it follows the traditional rules for creating a verb from a noun in Greek. Not meaning to totally shit on whoever originally put forward the idea, of course.
When is a loan word no longer a loan word? We could argue for days on this alone. If it is a loan word, what are the benefits of prescribing the use of the grammatical rules of the language it comes from over the use of the rules of the language in which it is being used?
Assuming we do want to adopt the grammatical rules of each language from which we borrow words, what does this mean for words that come into English via a whole bunch of different languages? A classic in Engish is where the verb form of a word came from Latin via French to English, while the noun form came directly from Latin. Would it not be more "correct" (if that's about consistency and clarity) to ditch one of these forms entirely and switch to both coming from either Latin or French?
And on and on it goes...
The other thing that becomes very clear in Linguistics is that people are naturally conservative about language change. Me starting this thread, knowing full well I have no way to justify (grammatically) anything I might rant about, is probably a good example of that.
