Asian parents are known for forcing their children to pick up sports and arts, so the musical art that stands out the most to the Indian parent is kind of naturally their own, which would be more familiar to them (additionally, since Indians tend to stick together - not particularly good for assimilation and integrating into the host country, I must admit - a parent might find it easier to enrol their child into Indian traditional music lessons through a friend of a friend). I don't think it arises from any notions of superiority - just a desire to stay close to the parent culture, I suppose.
I won't pretend to know everything about why Indians do certain things, but that's what I reckon, at least. I also mentioned in an earlier comment about how Indians who have recently (in the past 3-4 decades) settled abroad tend to maintain close contact with India and their family here - and many often come back later on, after working abroad for 10-20 years. You could probably label this close-mindedness and a failure to integrate, but for whatever reason, Indians tend to favour their own culture.