when countries like India that has existed since the beginning of civilization

Actually, the problem with Indian independence as that it wasn't one nation. The Americans were better able to band together because they came from a relatively homogenous socioethnic background and they saw themselves as brothers-in-arms. India, on the other hand, is much more culturally diverse. India has no single language or culture - there isn't even a majority except in individual regions. Although they're somewhat similar compared to rest of the world, a man from Mysuru and a man from Lucknow would have much less in common than a man from Hartford and a man from Atlanta. Even during the British conquest and subjugation of the Indian subcontinent, it was made up of groups of smaller states which each had their own language and culture. These differences made it harder for the Indian nation to find common ground among itself and unite against the British. Indeed, some of those cultural groups had been bitter rivals for centuries - and still were. One of the most interesting stories about India, actually, comes from its independence. A large state in the middle of India called Hyderabad refused to join the Indian nation. It ended up having to be invaded and annexed. Can you imagine an American Revolution in which Virginia or Pennsylvania rose up against the rest of the colonies?