Nicholas of Cusa writes:
the Koran says that the Virgin Mary, the mother of Jesus, was the sister of Aaron and the daughter of Amram. Now, it is most certain that the one who reported these [details] to Muhammad erred and was ignorant of the Gospel’s true narrative. For Mary the daughter of Amram and sister of Moses and Aaron was dead and buried in the desert more than a thousand years before [the time of] the Virgin Mary, the glorious mother-of-Jesus-Christ, who lived (as is read in this same Koran) at the time of Zacharias, the father of John the Baptist.
He is referring to passages such as Surah 66.12:
…Mary, daughter of Imran. She guarded her chastity, so We breathed into her from Our spirit. She accepted the truth of her Lord’s words and Scriptures: she was truly devout.
And Surah 3.35-36
Imran’s wife said, ‘Lord, I have dedicated what is growing in my womb entirely to You; so accept this from me. You are the One who hears and knows all,’ but when she gave birth, she said, ‘My Lord! I have given birth to a girl’– God knew best what she had given birth to: the male is not like the female–‘I name her Mary and I commend her and her offspring to Your protection from the rejected Satan.’
Imran is another way of saying Amram, who was the father of Miriam, Moses and Aaron:
And Kohath was the father of Amram. The name of Amram’s wife was Jochebed the daughter of Levi, who was born to Levi in Egypt. And she bore to Amram Aaron and Moses and Miriam their sister. (Numbers 26.58-59)
The author of these Qur’anic passages is clearly mistaken about just who Mary and Miriam are. As Nicholas writes: “And since the Koran makes these statements not once but repeatedly, this one example suffices [to show] that error is contained in [that] book and [to show] that therefore the authorship is not God’s.”
Islamic Response: Exegete Ismail ibn Kathir writes:
(O sister of Harun!) referring to the brother of Musa, because she was of his descendants. This is similar to the saying, `O brother of Tamim,’ to one who is from the Tamimi tribe, and `O brother of Mudar,’ to one who is from the Mudari tribe. It has also been said that she was related to a righteous man among them whose name was Harun and she was comparable to him in her abstinence and worship.
This response does not make sense in light of the Qur’an saying that Amram’s wife gave birth to Mary, not in some ancestral way, but directly.