Which sentence is correct?
- What are you talking about? I don't understand you.
or
- What are you talking about? I'm not understanding you.
Which sentence is correct?
- What are you talking about? I don't understand you.
or
- What are you talking about? I'm not understanding you.
Understand is a stative verb along with like, remember, think, want, etc. that is not normally used in the progressive form. This is why "I'm not understanding" is much less common than "I don't understand". However, as Huddleston in The Cambridge Grammar of the English Language (p170) states:
None of these (stative) verbs completely excludes the progressive. … The progressive adds an element of tentativeness. … It is not so clear how the politeness derives from the progressive. One factor is no doubt length/complexity: polite formulations are often more complex than ordinary ones.
The use of the progressive in the case of "I'm not understanding you" may also be interpreted here as implying that the failure to understand is a temporary state for which I, not you, bear the responsibility.
There is an extensive analysis of the various functions of the progressive (including tentativeness, politeness, deference, etc.) in Levin: The progressive verb in modern American English. Here is one extract:
… the progressive is used as a device that reduces imposition on the addressee.
meta: This may not be an answer.
One source says:
There are a number of verbs that can not be used in the Present Continuous. Th(ese are the) so-called stative verbs – verbs of state. (The) Present Continuous can only describe (an) action process that can start, pause or end.
(stative verbs:) know, believe, understand, recognize, realize, suppose, deny, imagine … [emphasis mine]
However, I think understand is a verb that can be used in a 'continuous' (dynamic) sense as well as a 'stative' sense. They mean different things and each may be suitable according to context.
Grammar Logs seems to think either is fine: I don't think there's anything particularly incorrect about "not understanding"; it's just silly.
C is definitely wrong. As you said,"understand" is a stative verb that should not be used in a progressive sense (though often is conversationally).
I don't think I will be able to provide a source to substantiate this answer, but the two sentences have the same essential meaning but differ in tone.
Grammatically, I don't understand you is the negative simple present tense indicative. I'm not understanding you is the negative present progressive indicative. Progressive tenses can have multiple meanings, but in this case, they have the same meaning.
The difference, at least as I see it, is where the two forms place the failure of understanding. I don't understand places the failure on your side -- failure to provide something I could understand. I'm not understanding places the failure in understanding on my side, implying I must lack something necessary for understanding. implies that I am experiencing a type of cognitive failure that prevents understanding. In other words, the present progressive identifies an I-state *I am ... * whereas I don't understand is merely a negation of the state of understanding...
C is wrong since it's not a word. It's two!