[Disclaimer: I know nothing about this, and am simply trying to understand a little. Don’t take this as authoritative or even reliable!]
Readers coming to the Quran from a Jewish or Christian background often expect it to be, like the Bible, primarily an account of events. They end up puzzled: why would a single story retold in many different places? Why would different épisodes from the same story be scattered across the book, with no one location giving a general summary? To begin to understand this, you have to realise that the story is being invoked in a surah-specific context, which determines what aspects of it are emphasised, and that you cannot expect the context to be immediately clear on a first reading. To make sense of it, you often need to look for external parallels to the story. Surat Taha is as good an illustration of this as any.
This surah must have come at a time when the Prophet and his still-young community were having a hard time, as its first line suggests – in particular, when he felt that he was unable to persuade enough people, and that even some of his existing flock were backsliding. Note that this retelling of the story of Moses emphasises Moses’ own feelings of inadequacy to the task; he asks not just for general help, but specifically for greater eloquence (and note the awkward verbosity of his speech as quoted prior to this prayer) and for his brother to be appointed to help him in his mission. He receives not just the help he asks for, but also the reassurance he wanted – a reminder that he wouldn’t even be here if it weren’t for God’s exceptional earlier mercy to him (compare Surat al-Dhuha) and that he had grown up only with his mother just as the Prophet had.
Pharaoh and his followers see Moses’ miracle, but take Moses for a magician to be vanquished by magicians. Likewise the Quran reminds us that the Prophet was accused of being a mere magician. But if transforming objects is the game of magicians, transformational words are normally the game of poets – and Quraysh got poets to challenge the Prophet just as Pharaoh got magicians. In the duel of the magicians with Moses, we see that humans can cause the illusion of transformation (“their cords and their staves, by their magic, appeared to him as though they ran”), but only God can cause the real thing (“he cast it down, and lo! it was a serpent“), which inevitably vanquishes the simulacrum. This applies well to words: note that the Qur’an’s objection to poets, seen elsewhere, is that they say what they do not do; their words project a mere image, failing to transform even their own speaker.