Moshe is referred to as eved Hashem, the servant of Hashem. Hashem is the owner having made a kinyan (act of acquisition) in Moshe. Moshe’s experience was very different from that of Avraham, who made a kinyan in Hashem, making Hashem his property.
However all this changed when the people sinned with the golden calf. Hashem tells Moshe the eirev rav, the non-Jewish multitudes that Moshe brought along from Egypt, caused this disaster. Moshe, Hashem says, you never sacrificed for the people, everything that you did as their leader was handed to you on a silver platter. Avraham built the nation, but you inherited it without any effort. You told Paroh to let the people go, and when he refused to recognize Hashem and acquiesce, Hashem supported you and sent the plagues upon Egypt. At the Red Sea, you simply raised your hand and the sea split. You have expended minimal effort on behalf of the people. On the other hand, Avraham demonstrated leadership when he tried to reason with Nimrod and was hurled into the furnace and when he placed his own life in jeopardy and interceded on behalf of the people of Sedom.
At the episode of the golden calf, Moshe forfeited his original leadership mission of taking the people out of Egypt, entrusted to him at the burning bush. If Moshe was unwilling to sacrifice himself on behalf of bnei Yisrael and accepted their destruction, he had to relinquish his leadership role. Ein melech bli am – there is no king without a nation. This message was delivered in a harsh tone, Vayedaber Hashem.
To this point, the patriarchs were greater than Moshe because of their dedication to building the Jewish nation and their willingness to persevere in that mission despite all sorts of hardships. Hashem hinted to Moshe that he could still save the people. Vayomer Hashem El Moshe, Hashem said to Moshe: you have lost a nation that you did not sacrifice for. At Har Sinai Hashem gave the Torah to the people. Moshe, you have not taught the people anything yet. However, now Moshe I have a new proposition for you. I offer you the opportunity to follow the footsteps of the patriarchs and work and sacrifice on their behalf. You have the opportunity to rebuild this people into the am Hashem. However, this time you will have to accomplish it without miracles, thunder or lightning. From now on you will have to travel the path of Avraham, a road riddled with obstacles and hazards, that will require great sacrifice on your part. You will have to educate them and persevere through their complaints and tribulations. The choice is yours. You can educate your own children (Gershom and Eliezer) to eventually become the am Hashem, and sanction the destruction of this group. Or, if you are willing to follow the path of Avraham and shoulder the responsibility for this group of idol worshipers and educate them to be shomrei Torah, then you can be their true leader. If you are willing to teach Torah to each and every Jew and show future generations the correct path, like the patriarchs were willing to do, then you have a chance to save them. But to do that you will have to become Moshe Rabbeinu, you will have to be their teacher.
When Moshe realized that the fate of the people was in his hands, he immediately replied zechor l’Avraham Yitzchak ul’Yisrael (shemos 32:13), I am ready to emulate the patriarchs and sacrifice on behalf of the nation. At the first kabbalas haTorah, Moshe had only to stretch out his hands and receive the luchos. At the second, Moshe had to hew the luchos himself and carry them up the mountain and carve their message into the hearts of the people. The first was between Hashem and all Jews, and was intended to make the complete Torah accessible to all Jews. The second was between Hashem and Moshe and required Moshe to become the teacher of the people. Chazal say that the first mattan Torah was to include all of Torah as Torah shebichtav. The second mattan Torah introduced Torah shebe’al peh, which required a Moshe Rabbeinu to teach to every Jew. Moshe had to accept this new and difficult role in order to save and rebuild the nation.