The problem is that India has many local languages. So you need one language, equally foreign to everyone (so no one has an unfair advantage) for things like federal laws, national-level competitive exams and inter-state communication (each state is, in theory, composed of the people speaking one language). English conveniently fits that bill.
We almost had civil war in the 1960s over this. The compromise was that (1) India has no national language, (2) all federal documents would be in both English and Hindi (the biggest Indian language) and (3) all schools must teach any three languages, including English.