Exode 4:10

And Mosheh said before the Lord, O Lord, I pray: I am not a man of words, nor ever have been before that Thou didst speak with Thy servant; for I am of a staggering * mouth and staggering speech. *Or, lame

AND MOSES SAID UNTO THE ETERNAL: O LORD, I AM NOT A MAN OF WORDS, NEITHER YESTERDAY NOR RECENTLY NOR SINCE THOU HAST SPOKEN UNTO THY SERVANT; FOR I AM SLOW OF SPEECH AND OF A SLOW TONGUE. “This teaches us that for an entire period of seven days, the Holy One, blessed be He, sat and urged Moses to undertake the mission. [The expressions], ‘yesterday,’ ‘recently,’ and ‘since Thou hast spoken,’ imply three days, and the three-fold word gam — [here translated ‘neither’ or ‘nor,’ but literally meaning ‘also’] — points to a similar extension of time. Thus you have six days [that have passed], and it was now the seventh day [when Moses still refused to go on his mission].” Thus the language of Rashi.
In line with the plain meaning of Scripture, the purport of the verse is as follows: [Moses said,] “For I am slow of speech from heretofore and from time past, for I have been slow of speech from my youth on and all the more now that I am old, and also now since Thou hast spoken unto Thy servant, for Thou hast not removed the defect in my speech when Thou didst command me to go to Pharaoh to speak in Thy name. How then can I go before him?” Now Moses out of his great desire not to go [on the mission] did not pray before G-d, blessed be He, that He remove his defective speech from him, but he argued: “Since You have not removed my slowness of speech from me from the time You spoke to me to undertake this mission, do not command me to go, for it is inconceivable that the Master of everything should send a man of uncircumcised lips to a king of the nations.” And since Moses did not pray [for the removal of his defect], the Holy One, blessed be He, did not desire to heal him. Instead, He said to him, I will be with thy mouth, and teach thee what thou shalt speak, meaning that “you will be able to correctly express the words which I will put in your mouth.”
And in V’eileh Shemoth Rabbah, the Rabbis said: “The Holy One, blessed be He, said to Moses: ‘Do not mind it that you are not a man of words. Have I not made the mouth of all that speak, and him that I desire I made dumb? And have I not made the deaf and the blind, and opened their eyes to see and ears to hear? Now had I wanted that you be a man of words, you would have been so. But it is my desire that you continue to be so, and when you will speak [to Pharaoh] your utterance will be correct, for I will be with thy mouth.’ This is the sense of the verse, Now therefore go, and I will be with thy mouth.”
According to this Midrash, it appears to me that the reason He did not desire to remove his defective speech from him was because a miraculous event, as told by our Rabbis, happened to Moses when he was still before Pharaoh.
The correct interpretation appears to me to be that G-d said to Moses, “Who hath made man’s mouth? or Who maketh a man dumb? … Is it not I the Eternal Who does all this? I could heal you. But now since you did not want to be healed, nor have you prayed to me about it, go and I will be with thy mouth, and I will cause you success in My mission.” It is also possible that there is a hint in the verse, And the anger of the Eternal was kindled against Moses, that He did not want to heal him, and that He sent him against his will.

כי כבד פה וכבד לשון אנכי, I am not fluent in the Egyptian spoken by the upper classes of the aristocracy. The reason is that I fled Egypt before I had completed my education there and in the meantime I am 80 years of age. We find in Ezekiel 3,4-6 that the prophet is told to address the Jewish people as opposed to addressing the local aristocracy whose tongue is described as unintelligible speech and difficult language, i.e. עמקי שפה וכבדי לשון. Is it possible that a prophet who could communicate with G’d freely, i.e. “face to face,” and who received the Torah from Him and communicated it to his people should have been afflicted with a stutter? [one could add to the author’s rejection of the commonly held view of Moses’ speech impediment that if he functioned as High Priest for a full week before his brother Aaron took over, how was that possible if he was afflicted with what would be considered a disabling mum, physical blemish for even an ordinary priest? Ed.] Nowhere in our traditional literature of Tannaim and Amoraim (Talmud) is there such a view expressed, and we certainly have no reason to accept such views when they are expressed in hagiographical writings.

לא איש דברים אנכי; I am not experienced in knowing how to address people in authority, such as kings.

גם מתמול, גם משלשום, neither when I was a stranger in a foreign land, nor when I grew up in Pharaoh’s palace, nor since You have spoken to me and I have responded.

כי כבד פה וכבד לשון אנכי, the reason why I do not possess this facility is because the physical tools with which to express my thoughts are defective. I have therefore never even made the effort to develop this facility (compare Isaiah 50,4) לדעת לעות את יעף דבר, “to know how to speak timely words to the weary.”

ויאמר משה בי אדוני, Moses responded by saying: בי אדוני, “please O Lord, etc.” Moses pointed out that he had been asked to face Pharaoh and his advisors who had command of all seventy languages, and would ridicule him when addressing him in any of these languages which he did not have any command of. They would then add: “In whose name and language do you come to speak to us?” G–d reminded him that it had been He who had enabled Adam to give the proper names in the in all the languages to all of His creatures. (Genesis 2,20) [It did not say there שם in the singular mode, but in the plural mode, i.e. that he named each animal in each of the seventy languages.] If He had been able to enable Adam to do this, Adam who had eaten from the tree of knowledge, it would require only a minor adjustment of Moses’ faculties for him to be able to do so also, and He implied that He would do so immediately, seeing that he had been selected to perform much greater deeds than had Adam. An alternate interpretation of G–d’s response: The words: מי שם פה, “Who has provided a new mouth, etc;” surely the One Who provided the first mouth in the first place at the time of creating human beings with a mouth to express their thoughts. (Attributed to Rabbi Yoseph.) Rabbi Ovadiah interpreted the answer as a rebuke to Moses, who was surely aware of G–d’s abilities, and if He had given Moses a mouth to speak with, He was surely also aware of Moses’ speech defect, and did not need a reminder from him. It is within My power to remedy this. [G–d did not say that He would remedy this, and if so when He would do so. Ed.]