Exodus 32:9-14 (NIV quoted):
9 “I have seen these people,” the LORD said to Moses, “and they are a stiff-necked people. 10 Now leave me alone so that my anger may burn against them and that I may destroy them. Then I will make you into a great nation.”
11 But Moses sought the favor of the LORD his God. “LORD,” he said, “why should your anger burn against your people, whom you brought out of Egypt with great power and a mighty hand? 12 Why should the Egyptians say, ‘It was with evil intent that he brought them out, to kill them in the mountains and to wipe them off the face of the earth’? Turn from your fierce anger; relent and do not bring disaster on your people. 13 Remember your servants Abraham, Isaac and Israel, to whom you swore by your own self: ‘I will make your descendants as numerous as the stars in the sky and I will give your descendants all this land I promised them, and it will be their inheritance forever.’” 14 Then the LORD relented and did not bring on his people the disaster he had threatened.
God threatens to destroy Israel, and apparently declines to do so because Moses mentions the promise God made to Abraham, Isaac, and Israel that their descendants would be numerous.
But this is exactly what God promised Moses to start with in verse 9—making a great nation out of Moses, who was a descendant of Abraham, Isaac, and Israel, would still fulfill the promise. So why does Moses' restatement of the promise have the desired effect? He doesn't have any other arguments than "what would Egypt think".