Moses is about to wrap up an entire chapter discussing why Israel doesn’t deserve to enter Canaan. By his own admission (and how he leads off the chapter), they aren’t going to inherit the Promised Land because they’re awesome, but in spite of themselves. They’re a stubborn people, after all (Deuteronomy 9:7).
In fact, they’re so rebellious that Moses has to intercede on their behalf personally to God.
This is a well-known characteristic of Moses; his role as a mediator is outlined in the New Testament as a type of Jesus (Hebrews 12:18-24). But did you ever stop to think about what Moses would even say to God on their behalf? After their rebellious stance with the golden calf, what kind of argument could he even make in their defense?
As it turns out, Moses has three distinct points to make concerning why God should not destroy Israel. None of them have to do with his own ego; instead, they talk mostly about God and the holiness of His name.
First, God has invested quite a bit of energy and capital into these people. He “brought them out with a mighty hand” and “redeemed them through His greatness” (Deuteronomy 9:26). Both of those were big shows of His glory that reverberated throughout the surrounding nations (Joshua 2:10).
Second, God had made a promise to the Patriarchs (Deuteronomy 9:27) which He could not break. If He didn’t bring the people into Canaan, how could any of us trust anything that God ever said about anything?
Third, and possibly the most harsh: If God destroyed the people now, then everyone else would say that God wasn’t able to control His own people (Deuteronomy 9:28). That’s not a reflection on them (they would be dead in that scenario, after all), but more on His abilities as a leader to corral Israel.
Those who think that God doesn’t care about the opinions of men should check this section out, because you can argue that the main reason God doesn’t annihilate Israel is because of what others would think about Him. His reputation matters a lot. As He stated in Exodus 9:16, God wants His name to be “proclaimed through all the earth.”
I’m not sure if Israel knew that Moses’ intercession was based on those three arguments, but if they did, they should count their lucky stars that God listened to the logic of Moses’ arguments. As he stated at the beginning of the chapter, it wasn’t their own righteousness that made God fulfill His promise, but His grace.
That grace would eventually run out with the Babylonian and Assyrian invasions, but this shows just how precarious their position was at the present moment.