For example:

He is very handsome. He cannot be your brother.


He is very handsome. He could not be your brother.

  • That seems to be an insult. I read both words as about the same. The word "could" sounds just a shade more natural. – Jack O'Flaherty May 15 '20 at 6:31

cannot is present tense, where could not is past tense. Of course in your example there is no real difference, after all if someone wasn't your brother in the past, he can't be one now either.

Makes more of a difference in cases where it can change with time.

"He cannot jump over the gap" - he lacks the ability today, and if he tried he would fall. "He could not jump the gap" - He used to lack the ability in the past, but he might have gotten better and can do it today.

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