Did the Messenger Muhammad learn to read and write after the revelation descended, and why is there insistence on describing him as illiterate?

Allah sent His Prophet Muhammad, peace be upon him, as unlettered, neither reading nor writing. This was a miracle and proof that what he brought was from Allah, not from himself, as stated in the Almighty's words: "And you did not recite before it any book, nor did you inscribe it with your right hand. Otherwise, the falsifiers would have had doubt."

Scholars differed on whether the Prophet, peace be upon him, learned to read and write after the revelation descended. One group said: He learned, citing the Hadith (definition) of the Treaty of Hudaybiyyah, where Al-Bukhari indicated that "the Messenger of Allah, peace be upon him, took the document and wrote." They believed that this does not contradict his being unlettered, but rather increases his miraculousness, because he wrote without prior learning. Another group said: He did not write a single letter, but rather he would order someone to write for him. They believed that his writing would contradict his being unlettered, and the verse refers to him not writing. This is the opinion favored by Al-Qurtubi.

And on both opinions, his description as unlettered is a miracle, for either his unletteredness remained with him until he died, or he remained characterized by it because it is one of his astonishing miracles and because he was sent to an unlettered nation.