Why did Muslims not want to be part of an independent India?

Well, I would say that Muslims have a different take on things and did not want to be associated with India. They wanted to have their own country so they can do whatever they wish (without control of india government). Muslims and Indians are in a conflict as of this moment. In short, Muslims did not get along with India.

India has a long history of inter-religious conflicts. Islam was brought to India by foreign conquerors. The Islamic Mughal dynasty ruled for several centuries, though it tolerated Hinduism. There are many historical grievances and old wounds. Muslims were afraid of persecution and exclusion in an independent, Hindu-dominated India. Besides, Muslims were a majority in some states and there were dreams of their own statehood. That's why partition occurred in 1947.