Because harry can carry through on his threats, and it seems the standard mental model for dementors has them being self-serving. A dementor should respond to threats, as far as I can tell.
When I was arguing this I was also taking into account that albus (and the great hall) had seen the dementor be afraid of harry, but it occurs to me that that was in the future.
Why does Albus have such a belief? He witnessed Harry kill a dementor, yes, but not control one.
That’s not to say that he would disbelieve that Harry could do it, but I see no reason for him to have a reason to “very very strongly believe” it.
Because harry can carry through on his threats, and it seems the standard mental model for dementors has them being self-serving. A dementor should respond to threats, as far as I can tell.
When I was arguing this I was also taking into account that albus (and the great hall) had seen the dementor be afraid of harry, but it occurs to me that that was in the future.