The mystery of why Number 6 resigned is that there's no mystery. What he was telling his superiors was the truth. Due to the cold war paranoia, they didn't believe him. There had to be some deeper mystery, he had to be part of some great conspiracy. So they spend the entirety of the series trying find out the answer to a mystery that's not a mystery.

No. 6 doesn't bother explaining to them since he's stubborn, hates them and gives a nice middle finger to authority.