What does "we never did" mean here?
Have we met?
We never did.
Does it sound natural to natives?
What does "we never did" mean here?
Have we met?
We never did.
Does it sound natural to natives?
The full form of the negative answer to the question "Have we ever met?" is "We have never met". You may leave out the participle "met", so long as you keep the auxiliary verb "have". This gives "We have never". But that word order is not idiomatic: the idiomatic word order is "We never have".
But you can't replace the auxiliary verb "have" with "do".
"We never did" would be a suitable answer to a question of the form "Did we ever ... ?". But the OP's question is not of that form.
We never did means the negative of the propitiation.
Have we ever danced?
No, we never did.
Have we ever had a discussion?
No, we never did.
Is there some confusion of the meaning?
Have we ever met?
No, we never did. = we never did meet.
You don't have to do this, but it is right, of course:
Person 1: Have we met?
Person 2: Yes, we have.
Person 1: When did we meet?
Person 2: We met last week.
You can answer with the shortened form auxiliary from the simple past:
Person 1: Have you (ever) gone to Rome?
Person 2: No, I never did. [I never did go to Rome.]
Person 1: Have you ever read any Dickens?
Person 2: No, I never did. [No, I never did read any Dickens]
It's fine. In these kinds of contexts, you can switch tenses and auxiliaries as shown above.
And this is not a BrE/AmE thing. It is something that happens in both.
Dialogue _ Full use of verb tenses:
Person 1: Have you had problems with your car?
Person 2: Yes, I have.
Person 1: When did you have problems with your car?
Person 2: I had them last week but I don't now.
Dialogue _ Shortened form:
Person 1: Have you had problems with your car?
Person 2: Yes, I have.
Person 1: When did you have problems with your car?
Person 2: I had them last week but I don't now.
Another example:
Dialogue _ Shortened form:
Person 1: Did you see your parents yesterday?
Person 2: No, but I will tomorrow.
[for: No I didn't. But I will see them tomorrow]
Final example from me:
Person 1: Are you cooking tonight?
Person 2: Well, I might.
OR
Person 1: Are you cooking tonight?
Person 2: No, I cooked yesterday.
It's fine to shift tenses like that in speech.
This is completely idiomatic in English.