[cadabrabra]

It’s a common confusion, often subconsciously deployed in the context of trying to cope with the possibility of something undesirable turning out to be true.

[pfdietz]

It's also important to distinguish "I don't believe X" from "I believe not-X".

English is poorly suited to expressing this distinction.

[buttstuff69420]

No. What happened here is you confused semantics for logic.