In the name of Allah, the Beneficent, the Merciful
The Quran refers to Mary, upon her be peace, as the “sister of Aaron” in reference to her descent from the lineage of the Prophet Aaron, upon him be peace. This type of reference is common in ancient Semitic languages and in the Bible.
يَا أُخْتَ هَارُونَ مَا كَانَ أَبُوكِ امْرَأَ سَوْءٍ وَمَا كَانَتْ أُمُّكِ بَغِيًّا
O sister of Aaron, your father was not a man of evil, nor was your mother unchaste.
Surah Maryam 19:28
The Christians at the time of the Prophet objected to this verse on the grounds that it was meant literally, but the Prophet answered their question.
Mughira ibn Shu’ba reported: When I came to Najran, the Christian monks asked me, “You recite the verse: O sister of Aaron (19:28), whereas Moses was born long before Jesus by such-and-such years.” When I came back to the Messenger of Allah, peace and blessings be upon him, I asked him about it and he said:
إِنَّهُمْ كَانُوا يُسَمُّونَ بِأَنْبِيَائِهِمْ وَالصَّالِحِينَ قَبْلَهُمْ
Verily, they would name people with the names of prophets and righteous people who had gone before them.
Source: Sahih Muslim 2135, Grade: Sahih
Ibn Kathir reported:
علي بن أبي طلحة والسدي قيل لها يٰأُخْتَ هَـٰرُونَ أي أخي موسى وكانت من نسله
Alli ibn Abu Talha and As-Suddi said: It was said to her: O sister of Aaron (19:28), meaning the brother of Moses because she was from among his descendants.
Ibn Kathir added:
كما يقال للتميمي يا أخا تميم وللمضري يا أخا مضر
This is like saying to somebody from the Tamimi tribe: O brother of at-Tamim, or to somebody from the al-Mudari tribe: O brother of Mudar.
Source: Tafseer Ibn Kathir, verse 19:28
Muhammad Asad comments on the verse, saying:
In ancient Semitic usage, a person’s name was often linked with that of a renowned ancestor or founder of the tribal line. Thus, for instance, a man of the tribe of Banu Tamim was sometimes addressed as “son of Tamim” or “brother of Tamim.” Since Mary belonged to the priestly caste, and hence descended from Aaron, the brother of Moses, she was called a “sister of Aaron,” in the same way as her cousin Elizabeth, the wife of Zachariah, is spoken of in Luke 1:5 as one of “the daughters of Aaron.”
Source: Message of the Quran
Therefore, the verse is not a historical mistake, but rather it is in perfect agreement with the Semitic languages and ancient custom.
Success comes from Allah, and Allah knows best.