Why is clarity called the "door-opener" among the intellectual standards?

Because without clarity you literally cannot tell whether a statement is correct or important — every other check depends on first understanding what was said.

Clarity (Klarheit) is foundational: you can't judge whether a claim is accurate, relevant or deep until you actually understand what it asserts. An unclear statement blocks every downstream assessment, so it has to be resolved first.

The practical moves to force clarity are questions:

• "Could you develop that thought further?"
• "Could you put it in other words?"
• "Could you give me an example?"

Tip: This is why clarifying terms is step one in examining any truth-claim — an ambiguous claim isn't even wrong yet, because you don't yet know what's being claimed.