Why is Europe a continent? Why isn’t it just part of Asia? I don’t get it.
Its a matter of geology, not contiguous terrain. India, for example, is sort of the same thing, but its further along than Europe. I think that either Europe is sliding over or under Asia, much the same as India.
The Perfect Master has dealt with this question here.
That’s good enough for me.
Thanks
As Cecil noted, it started with the Greeks. They were the first group (that has passed us a legacy) that spent any serious effort on geography. They could see that the peninsula on the West and North of the Aegean Sea was part of one land mass and that the area East of the Aegean and South of the Black Sea (and connected by the Dardanelles, Sea of Marmara, and Bosporus strait) was one land mass. They also knew that the Red Sea and Bay of Suez mostly separated Egypt and points West and South from the area they had named Asia. So they gave each of them names.
Later, as Europeans set out to conquer the world, they saw no reason to share their “continent” with the people to the East, so they drew a line down the Urals and called that a boundary for Asia and Europe. (Meanwhile, the original Asia got down-rated to Asia Minor.)
If we can call one part of Eurasia “the Indian subcontinent”, we can damn well call another part of it “the European subcontinent”. Fair’s fair. 
Calling India a “subcontinent” has a real geological basis, though. The Indian peninsula is a separate continental plate, which was orignally separate from Eurasia. It’s the collision of the two plates which is raising the Himalayas (so far as I know, they’re still growing). By contrast, there’s no geological disctinction between Europe and Asia.
If we’re going to go on the basis of real geology, then Italy and Spain would be part of Africa and the Middle East would be a separate continent.
From what I understand, Europe was not always part of Asia, but rather collided with it as India did. The Urals are an ancient range similar to the Himalayas in that they were pushed up by the collision. But unlike India, the collision stopped happening and the Urals have been eroding ever since. The Appalachians are a similar range, being where North America pushed into Europe hundreds of millions of years ago.
But what does this all have to do with modern geography?