I would have chosen "can". This is the most idiomatic, but it has little to do with logic, or the meaning of "be able".
The reason is subtle and seems to be connected to the fact that a person has a free will to choose to be disobedient. Modals like "might", "may" or "will" assume that disobedience is a the result of some automatic or random system, something that is out of the control of the individual.
He will be disobedient. -> A certain prediction, there is nothing that he can do to prevent it.
He may be disobedient -> There is a random chance of disobedience, again this suggests that he has no control.
He can be disobedient -> He will be disobedient only if he chooses to be disobedient.
Using "can" like this is personifying, it makes an inanimate thing seem to act like a human.
This computer program can crash sometimes. (Suggests that the computer is like a person and crashes when it chooses to)
Your posted picture is irrelevant, since it doesn't deal with people choosing to be difficult but is examples of the idiomic "it may be difficult (to do something)"