McGahn recognized the key fact—that Trump wanted to fire Mueller for the wrong reasons. Trump wanted to fire Mueller because his investigation was threatening to him. This, of course, also illuminates the reasons behind Trump’s firing of Comey, which took place just a month before the President’s confrontation with McGahn regarding Mueller. Trump and his advisers have offered various tortured rationalizations for the firing of Comey—initially, for example, on the ground that Comey had been unfair to Hillary Clinton during the 2016 campaign. Trump himself came clean in an interview with NBC’s Lester Holt and in a meeting with Russia’s foreign minister. In both, Trump acknowledged that he fired Comey to stall or stop the Russia investigation—that is, the investigation of Trump himself and his campaign.
This was an improper purpose, and McGahn clearly saw that the same improper purpose underlay Trump’s determination to fire Mueller. So McGahn issued the ultimatum that prompted the President to back down.
Mueller and his team surely have evidence on obstruction of justice that has not yet been made public. But even on the available evidence, Trump’s position looks perilous indeed.