When the continents were forming, India was a separate island. Slowly, it moved towards the rest of Asia, finally crashing into it, pushing up the Himalayas. Also, it still is a rather large piece of land sticking out of Asia with a boundary in between in and Asia, and it is more like a giant peninsula which isn't really completely part of Asia because it attached on much later after Asia had already formed. Thus, it can only be partially considered as a part of Asia as it was on its own for a long time.