Because they form the same premis.
The same sentence.
I could write a sentence with a thousand clauses and a thousand verbs without one canceling each other out. That two negatives occur in the same sentence does not mean they cancel. Double negative which cancels must first and foremost be in the same clause.
For reference please think of this:
John has never seen a movie.
John did not watch a movie that did not have a swear word.
This sentence is true. This sentence claims that John has not seen a movie that contains explicit language.
If we cancel the negatives we are left with
John watched a movie with a swear word.
This cannot be true because John has never seen a movie.
Now compare
John has not had a belief
John did not believe that God does not exist.
The same is true here with negation. That is because how this sentence is what John did not believe was the assertion that God does not exist.
Any belief you put after John did not believe must be true because John has not had a belief.
The assertion God does not exist, is a belief.