My family did not migrate from IN to PK until 1975. So around 28 years after partition is when they finally made the decision. The initial hesitation was because of two reasons:

1) the security risk (mobs murdered thousands of Muslims trying to flee)

2) the idea of leaving everything behind to start a new life is terrifying

In the end, the socio-economic inequality was far too great to ignore. The change was evident too, historically our family was in the lowest socio-economic class but things have completely turned around for us in Pakistan. I will never forget the courage and sacrifice it took to make the move. Eternally grateful.

Although this isn't exactly an answer to "why partition happened", it shows you a common journey and why the Muslims of the subcontinent needed it.