After the tragedy involving the עגל מסכה (commonly, but imprecisely referred to as the sin of the golden calf), Moshe engages in a series of dialogues, or negotiations, with Hashem. These negotiations take place in two rounds, each with its own focus. The first set centers on literally saving the Jewish people from imminent destruction by Hashem (פרק ל"ב שמות), while the second set involves Moshe's effort to win a commitment from Hashem to rejoin the Jewish people in their travels and dwell within them ( שם פרק ל"ג). Both cursory and detailed analyses of these negotiations indicate that, at least in part, Moshe succeeded. After all, we are here today to discuss the story. How is it possible, though, that a mortal (great as Moshe may have been) could actually influence the Master of the Universe?
Those familiar with the words of Rashi know that he actually anticipated the question. In his comment on a Posuk which presents Hashem's threat to destroy the people (שם ל"ב:י'), he observes that in informing Moshe of the travesty committed by the nation, Hashem was actually opening the door for Moshe to stand in defense of the people. The invitation inferred by Rashi, though, is still insufficient, as it extends only to Moshe's right to prevent the total annihilation of Am Yisrael. Moshe, on the other hand, takes liberties with his license and repeatedly returns to negotiate for more concessions from Hashem.
Moshe is not the first to engage in this type of activity. Avraham, upon being informed of Hashem's intentions regarding Sedom, stands in front of Hashem and tries arguing on behalf of the five towns of Sedom, apparently without invitation and certainly without success (בראשית י"ח:כ"ג-ל"ג). Interestingly, there is no indication that Hashem is displeased with either Avraham's or Moshe's intercessionary activities.
Not only is Hashem not displeased, but one may suggest that their efforts are precisely what Hashem had hoped for. In classical Midrashic thought, it is this element of defiance, this fighting spirit, that separated Noach from Avraham - one sitting passively and watching the Divine destruction of humanity, the other fighting it with every fiber of his being.
In fact, perhaps it is Moshe's unwillingness to simply accept decrees upon him that make him so desirable in Hashem's eyes as a leader. From the time we meet him, Moshe is defiant. In Egypt, he defies conventional norms of right and wrong. In Midyan, he defies and confounds the local shepherds. At his first encounter with the Divine on the mountain, he refuses to accept his mission, and upon his return to Egypt he regularly defies the king. As a man of principle, Moshe must be willing to be defiant. Hashem knows this, and desires this quality - for it is only the man who has the courage to stand alone defending his principles who can honestly lead his nation into a reality so fundamentally different from the one they already know.
Moshe didn't need to be invited to argue with Hashem - it was his nature. Hashem told him to leave the mountain, but Moshe refused to budge until he was reassured of the security of the Jewish people. His continued defiance is not really defiance at all - to the contrary - it is the fulfillment of Hashem's true wish. And just what is Hashem's true wish? That the leaders of the Jewish people feel their responsibilities so profoundly that no obstacle, not even Hashem Himself, will stand in the way of their defense of their nation - His nation.