The simple answer to your question is that none of the Islamic rulers of india were speakers of Arabic. This of course is primarily true of north and eastern India as the invasions usually came from Central Asia. As for the south of India, this in reference to the western coast of the Indian peninsula the interaction with the Arabic speaking world was mostly through trade. This while did spread Arabic as a link language for traders and as a religious language for local muslims did not spread as a language of state. In the north the initial invasions were by the Ghaznavid(11th century) and Ghurid(12th century) raids of the subcontinent. The Ghaznavids were , despite their turkic origin persianised. The Ghurids too were of Iranian origin. Neither of these groups created lasting state systems that had a significant language policy. The succeeding Islamic states that formed in India were from the slave dynasties(13th century) and later the Delhi sultanates. They too were speakers of Persian languages. The other invasions that happened during this periods include the invasion of the mongols and Timur(14th century) who were central asian in origin and thus did not speak Arabic. Babur(1483-1530) who was from Timur's lineage and would go onto to begin the Mughal empire was from fergana valley in central asia. His memoirs were written in the Chagatai languge. Persian was later accepted as the court language of the Mughal empire and a significant portion of the officials of the empire of different religions did learn it. Despite this Persian was never expansively used outside of the court and a series of regional languages survived along with it. Considering parts of southern and north eastern india (except Assam) fell beyond the influence of Mughal rule the influence of Persian was limited in these regions. This does not conclude though that Arabic did not have a presence in India. I was merely not used as a language of state by any of the Islamic empires. Some exceptions to this can be seen in examples like the umayyid invasion of sindh in the 8th century, but this does not seen to have left a significant imprint on the spread of arabic in India. As mentioned earlier trade was a significant area in which arabic was used, so was religious practice. These are the two fields through which arabic has had and still does have a presence in India.

References:The Mughal Empire (The New Cambridge History of India)

The Delhi Sultanate: A Political and Military History (Cambridge Studies in Islamic Civilization)

Objects of Translation: Material Culture and Medieval "Hindu-Muslim"

Islamic Central Asia: an anthology of historical sources

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!