In an answer to the question why the President would not just fire the Attorney General a user explained that after a (requested) resignation the President could appoint a temporary replacement whereas after a dismissal, this might not have been the case and the deputy AG would probably have taken over. This leads to ask the question from the other point of view:
- What can a cabinet member gain from actually resigning after being asked to by the President?
- What could a cabinet member lose if they chose to wait for the President to fire them?
There are some obvious points:
- Some might argue that it's always better to resign than to be fired. However, I do not think that a former cabinet member will ever have to apply for a job like "normal" people do. And, even if being fired by the President probably disqualifies you among people supporting that President and/or their policy, it might just as well be well received (or at least unimportant) among their political opponents.
- Cabinet members should be loyal and thus not refuse to resign after being asked to by the President. However, they might consider the reason for the request as being morally and/or legally wrong and thus stay in office "for the best of the country" (in their opinion).
- One might not want to continue working with a boss who asked them to resign. In the specific case of former AG Jeff Sessions, I believe that the relationship between the two men has already been suboptimal (to say the least) for quite a while and it did not seem to bother the AG enough to resign.
The question's aim is not to speculate about Mr. Sessions' personal reasons, but to give clear-cut reasons, possibly based on precedents, laws and/or regulations, or also interviews with and/or biographies of retired or dismissed cabinet members.