I don't understand about "Not with that attitude they don't".
Shouldn't "Not with that attitude" follow by "they do"? In my understanding, "Not with that attitude they do" means "If they don't have that attitude, they do succeed". But people are using negative term "they don't/can't/won't" following "Not with that attitude", is that because of grammar?
"Not with that attitude they don't".
That expression can be paraphrased as "They don't, especially not with that attitude." The negations reinforce each other, and both are required for the expression to make sense. You can consider it an idiomatic structure, and you can't pick it apart with logic.
It would greatly help if you gave some context. "Don't" what?
And meaning comes before grammar always. What you intend to say determines what grammatical form is required.
The common locution
Not with that attitude, they won't
does mean
They won't with that attitude
and so does violates the grammatical rule about double negative.
But if you use a common locution and change its form, no one will understand you. Moreover, the locution frequently is used in answer to a question.
Will they win?
No, they won't. Not with that attitude.
is really repetition of the same negative rather than a double negative.
