Moshe repeats that he has a speech impediment in Shemos 6,12 because it is part of his argument to Hashem that Pharaoh would not hearken to him, as it says: "And Moshe spoke before Hashem, saying: Behold, Yisrael did not hearken to me, how then will Pharaoh hearken to me, seeing that I am of closed lips?".
The sefer Binyan Ariel explains Moshe's argument was as follows:
When Hashem told Moshe to go together with Aharon because he was "heavy of tongue" and also to accord honor to his older brother, Moshe understood that they were supposed to speak together, as it says in the Mechilta on the posuk in Shemos 12,3: "Moshe accorded honor to Aharon, and Aharon accorded honor to Moshe, and it seemed as if the speech came from both of them".
But the gemara in Rosh Hashanah 27a says that two voices speaking simultaneously cannot be heard very well, unless it is something that the person listening really wants to hear. This was Moshe's argument, that if Yisrael were not able to hear us because we were speaking together, even though we were telling something that they really wanted to hear, how is it possible that Pharaoh will hear us, "seeing that I am of closed lips". That is, since Moshe had a speech impediment and thus always spoke together with Aharon as per his understanding of Hashem's instructions, if Yisrael were not able to hear them, all the more so Pharaoh would not be able to hear them. Therefore, Hashem now clarified to Moshe that he was to speak first and then Aharon by himself.
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