You're making a false (but commonly held) ahistorical assumption that China was always unified as a nation since the Qin. But that isn't true at all. Following the collapse of the Han Dynasty, China fell apart into dozens or more mini-kingdoms for over 300 years; and broke up again when the Tang fell in the early 900s. Probably what we think of as recognizably "Chinese" finally takes root in the Song, though thereafter China was ruled by foreigners-Mongols and Manchus.

China and India are extremely different in that China is a more unified society in terms of language and culture. To this day, dozens of languages and hundreds of dialects exist in India. In fact, almost every Indian state has its own language. This barrier to territorial and societal unification was one of the biggest reasons that India hadn't been unified. In fact, the idea of being "Indian" was not set in stone until the British unified the subcontinent as a colony and independence movements sprung up. The territorial and linguistic division of the subcontinent that has been present throughout most of history was not a detriment to its technological, societal, cultural, or religious development, for the most part. However, this division made it easier for the British imperialists to colonize India (divide and conquer).