I think it might be borderline arrogant of him to think that his threatening to resign would be seen as undesirable enough by Command and the Federation President that they'd just give in... but I would say this might also be justifiable. In 2385, Jean-Luc Picard very clearly is a famous officer with a great deal with political clout. He was commanding officer of consecutive Federation flagship for almost twenty years, he's saved the Federation and its capital planet on multiple occasions, and he's had major influence on the political situation in local space (he installed Gowron as Klingon Chancellor, then his officer Worf installed Martok; he made first contact with the Ferengi; he helped get the ball rolling on establishing a Federation presence in the Bajor system after the Cardassians withdrew; etc.). When the Mars Attack happened, FNN threw his name and reaction all over the news. In 2385, Jean-Luc Picard is a big deal. He's arguably the Dwight D. Eisenhower (pre-presidency) of the Federation.