Your logic is fundamentally flawed.

私有製是腐敗的禍根，that is A(私有製) -> B(腐敗). If it is true, then not B -> not A also true. But not A -> not B may not be true.

What you said: 北朝鮮沒私有製(not A) ，沒此禍根，應該沒腐敗 (not B).

This is high school stuff. Hope it is not too much for you to understand.