The following sentence, which doesn’t make much sense, was uttered by a non-native English-speaking English professor.
"What does the reason people learn a foreign or second language have to do with this course?”
I can figure out what he or she was trying to say. But if I were him or her, I would rephrase my sentence and say something like: why should people learning a foreign or second language have to take this course?
Yes, it is correct. I'll break it down so it's easier to understand.
The structure of the sentence is:
What does X have to do with Y?
where X and Y are both noun phrases.
It means, "What is the connection between X and Y"?
People usually say this when it's unclear why somebody is talking about something when it seems irrelevant to the situation.
In that sentence, X is this long noun phrase: "the reason (that) people learn a foreign language".
So it means, "What is the connection between this course and the reasons people learn new languages?".
Yes, it is correct. It is correct to say “What does (A) have to do with (B)?”
In this case, A is a bit long and complicated - “the reason people learn a foreign or second language” - but there is nothing grammatically wrong with it.
If a native speaker wrote that, I’d take it as a rhetorical question, very similar to, “The reason someone wants to learn a second language has nothing to do with this course. Isn’t that correct?” It’s something I might say if I didn’t want to answer a personal question, and didn’t care about being polite.
But it really depends on how you say it. If you emphasized the word does, making the question, “What does the reason we want to learn a second language have to do with this course?” it sounds more like a sincere question: “I believe you that these two things are related, but how?” Emphasize the word this, before course, and the question is asking, “There is another course where that question would be more appropriate, isn’t there?” Emphasize the word foreign, and the person is wondering why he or she is being questioned specifically bout learning a foreign language. And so on.
There are several different things the person could be trying to say, and it can be difficult to tell which one the other person meant.
Both answers already given are correct. What does X have to do with Y? is the basic pattern. However, some languages are more comfortable than others with X and Y becoming long and convoluted themselves in such patterns. As X and or Y becomes longish, English generally prefers to untangle the sentence and go for a more straightforward alternative construction. I could have said "native English speakers prefer..." but that might imply a conscious choice, whereas we are just talking about a general sense among native speakers of what sounds more natural.
In this particular case, a minimal choice that renders the sentence much more straightforward would be What does this course have to do with the reason why people learn a foreign or second language? but it is still a borderline case of what having to do with can mean. Slightly more natural is How does this course relate to the reason why people learn a foreign or second language? --- and of course OP's paraphrasis is far more natural still.
