I don't know when the earliest reference of India as "the Subcontinent" is but in modern times, its geology. Current plate tectonics hold that India was at one point its own continent that slammed into Asia and fused with it. This impact actually created the Himalayas.

The Indian Subcontinent doesn't just include India. The British, who first popularized the term, included (what are presently) India, Pakistan, Bangladesh, Nepal, Sri Lanka and Afghanistan under the term "Indian Subcontinent". Taken together, it's about half the size of China. For that matter, Russia is about twice the size of China, but it's not called the "Russian Subcontinent" either.

Since this nomenclature predates the discovery of plate tectonics, I don't think arguments based on geology are applicable. I think the traditional sense of the term "subcontinent" is more applicable, that is, a large area that is geographically more or less independent of the rest of the continent. The Himalayan range is a huge barrier that has separated cultures and people across it, and led to distinct divisions in people, languages and shared histories.

Continents, ergo sub-continents, are a product of opinion. Europe is a continent but why? Continents don't actually have any firm scientific definition. They are a product of mostly irration human judgement. India is a sub-continent because they are ethnically and culturally very different that China or indo-China. As well, geologically, they crashed into Asia.