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This is an allusion to the aspersions occasionally cast upon Moses by some of his followers and mentioned in the Oid Testament (e.g., Numbers xii, 1-13), as well as to the blasphemous demands of which the Qur'an speaks - e.g., "O Moses, indeed we shall not believe thee until we see God face to face" ( 2:55 ) or, "Go forth, thou and thy Sustainer, and fight, both of you!" ( 5:24 ). These instances are paralleled here with the frequently cited accusations that Muhammad had "invented" the Qur'an and then falsely attributed it to God, that he was a madman, and so forth, as well as with frivolous demands to prove his prophethood by bringing about miracles or - as is re-stated in verse {63} of this surah - by predicting the date of the Last Hour.
The Quran does not specify how Moses was slandered by some of his people. Some narrations suggest that he was either falsely accused of adultery (see footnote for 28:76), killing his brother Aaron (who died a natural death), or having a skin disease since he, unlike others, used to bathe with his clothes on.
The people of Moses often vexed him and rebelled against him and against God's Law. Here the reference seems to be to Num. xii. 1-13. It is there said that Moses's own sister Miriam and his brother Aaron spoke against Moses because Moses had married an Ethiopian woman. God cleared Moses of the charge of having done anything wrong: "My servant Moses is not so, who is faithful in all mine house." Miriam was afflicted with leprosy for seven days as a punishment, after which she was forgiven, as also was Aaron. This is the Old Testament story. The holy Prophet was also attacked because of his marriage with Zainab bint Jahsh, but not by his own circle, his motives were of the highest and were completely vindicated as we have seen above.