I think the best representation of “Demon/Devil logic is not mortal logic” is this scene here in Hereditary (2018).
When confronted with the fear and panic of their lives being taken over by a supernatural entity, mortals will attempt to rid themselves of the terror by trying to destroy whatever it is that binds that entity to the mortal realm. It could be a lock of hair, a journal, an amulet, etc.
In Hereditary, the mother Annie attempts to throw her deceased daughter’s sketchbook into the fire when she sees disturbing images in it. She immediately catches fire and recognizes that the book is linked to her and believes her daughter’s spirit is angry with her.
As the plot thickens, she begs her husband, a psychiatrist, to burn the book as she feels that it is the only way to get rid of the demon Paimon that is taking over their lives even at the cost of her own life. But as the book burns, her husband is the one that catches on fire.
No matter how logical a mortal attempts to deal with and fight a demonic supernatural entity, their human logic will always be illogical in the presence of an entity that operates by their own type of logic.
That is that whatever the situation, their choices are not for them to make. And whatever logic they attempt to use to remedy the situation will always be in vain and futile.
When demons want to play, you don’t get a say in the matter. Even if you weren’t the one to start the game.