A variety of reasons -- mostly incompetent governance, but the main root cause is that India is technically not a country, but a continent with myriad different groups. In many ways it's like a larger version of the European Union with the added effect of different races (95% Caucasian + 5% Mongoloid --> and of the 95% Caucasian, 3/4ths are Indo-European and 1/4th are Dravidian)
Some parts of the country like Kerala have 100% literacy while others like Bihar have only 70%. Some places have high-tech industries while others like the Jarawas live in the stone-ages on the Andaman islands.
People can freely move from one place to another and so it's not that easy to make one area alone, rich
However, as a whole, the country is progressing, slowly.
Also, note that they were socialist for 40 years after independence and are not completely market-oriented yet, which is another drag on their economy
In agreement with your post.
The development of India and China is one of the reasons the global economy boomed in the last thirty-forty years. Think about it. Up to about 1980, both countries, with about one-third the world's population, were mired in socialist economies preventing appreciable contributions to the world economy except in exports of raw materials. Then both plunged headlong into the free-market/capitalist system (to a certain degree) which has allowed both countries to gain substantial footholds or primacy in the global wealth race.
In fact, many experts expect China to overtake the U.S. before too long. That's in part because many Americans want to plunge America into a socialist paradigm which the two previously socialist countries have mostly succeeded in escaping. Which allowed sizable percentages of their people to live lives undreamt of by their previous generations. Life sure is strange.