Simple answer is wealth. Western countries, on average, are wealthier than most Asian countries. Credit where credit is due. The wealthiest Western countries are wealthiest in the world. So, this means higher quality of life and standard of living for those living and working in these nations.

An analogy on a smaller scale would be rural people moving to cities for opportunities. As long as the West is the wealthiest in the world, there would be ambitious people who would want to take full advantage of the resources and opportunities offered here.

BUT, this is starting to change as Asia gets wealthier. There would be less reasons to emigrate. Why be a second class citizen in a foreign country when you can live a decent life at home?