Most Indians, however, don't consider themselves Asian, they consider themselves Indian. India is considered a sub-continent. I don't really know what a sub-continent means, except "we're not Asian."
In the same way that Europe is considered distinct from Asia, despite the fact that it's all one contiguous continent. They just make the boundary between Europe and Asia be the Ural Mountains. Similarly, the Himalayan Mountains form an effective boundary between India and the rest of Asia