ויען משה ויאמר והן לא יאמינו לי ולא ישמעו בקלי כי יאמרו לא נראה אליך ה'
And Moses answered and said: "But they will not believe me nor listen to my voice; for they will say: 'The Lord has not appeared to you.'"The repetition here requires explanation. If it already says that they will not believe him, then how is it an explanation that they will say "The Lord has not appeared to you"? It doesn't seem to add anything to the discussion, which as the commentators point out, is already odd because why would the elders fail to believe in prophecy.
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I think we can answer this based on a distinction the Rambam makes in his introduction to his commentary on the Mishnah. The Rambam asks how Ya'akov could have been scared that God would not protect him (Gen. 32:8) when God had promised that He would (Gen. 28:15). We know that any prophecy for the good must come true even if the intended recipient sins and no longer deserves the good (Berakhos 7a), so Ya'akov had an unquestionable divine assurance that he would be protected.
The Rambam explains that we have to distinguish between a public prophecy -- those that a prophet is commanded to tell other people -- and a private prophecy that God tells the prophet for his own personal knowledge. A public prophecy for the good will always come true but a private prophecy for the good may not if the person sins and no longer deserves it. A public prophecy must come true because otherwise there would be no way left in which we can prove a prophecy to be true. However, a personal prophecy, one given to the prophet for himself, does not need to be proven because he knows that God spoke to him.
Moshe was unique in many ways and it seems to me that one of them is that he was the first to receive a public prophecy. The Patriarchs only received private prophecies. This prophecy to Moshe at the burning bush, in which he was told to go the Jewish elders and command them to go with him to Pharaoh, was the first public prophecy. God told it to Moshe and Moshe was supposed to tell it to others.
This is the aspect that the elders would find difficult to believe. If God wanted to contact them, why didn't He have them prophecy directly like He did with their ancestors, the Patriarchs? If God had a mission for them, why didn't He tell it straight to them? They would have found it difficult to believe that God spoke to Moshe, to say something to them. Their argument would be "The Lord has not appeared to you" -- to you and not to us.
What the elders, and the entire nation, needed to learn is that in order to move from being a family to being a nation, they needed to centralize their authority. They needed a chain of command and a leader. Like we later see with Korach, it is not enough for the entire nation to be holy and for God to speak directly to each one of them. Instead, He chose a leader and spoke to him, who then spoke to the leaders below him, who continued to communicate the message down the ladder.
And perhaps this can be seen in the three proofs that God has Moshe show them (Ex. 4:2-9). The first is turning Moshe's rod into a snake; the second is making Moshe's hand leprous and then healing it; and the third is turning water from the Nile into blood. There are other times when God send messengers to teach people a lesson. One type of messenger is natural disaster, particularly animals who injure and kill people. Another type is the exact opposite, doctors who heal injuries. But an even more basic messenger is the nature -- the water that nourishes the trees and vegetables -- that feeds and sustains us. Destruction, salvation and sustenance all come from God, and they usually come through messengers He sends and not directly from Him. With the first proof, God was telling the Jewish elders that He sends animals as messengers of destruction; with the second, that He sends healers to cure the sick as messengers of salvation; and with the third, that He sustains us daily through the miracles of nature. Similarly, He was sending Moshe as a messenger of prophecy.