The narrator says he resigned do to persistent questioning of his handling of this crisis. Though he did have a major gaffe on the succession question, his resignation was more a response to his handling of the Falklands Island war and his insistence of always being in the middle of each foreign policy decision.
As I remember.
"It's the system, Lara. People will be different after the Revolution."
One misreported aspect of the Reagan pres' is that he was both loved and respected by his cabinet and others working under him. It wasn't true. Most either tendered a resignation or threatened to. George Schultz three times.
Haig and Stockman left in the first term. While RR was loath to take a resignation from anyone he took these two without much of a fight. His kitchen cabinet from Cal didn't like them (they didn't like most Cab'members). Haig's biggest complaint was that he just couldn't get any time with the president or interest him in anything.
Kisskiss, Bangbang