Hyderabad acceded to Pakistan. Why wasn't that area given its rights? But that was wrong because the majority of Hyderabad wanted to join India. Kashmir is a similar case.Kashmir became part of India when the accession was approved by the king. From that moment, Kashmir belonged to India and Indians, including the new Indian Kashmiri citizens. Why should a large percentage of the population loose land because of a few? We have to consider the needs of the majority. They can have Kashmir as a part of India or they can be stateless people. Their choice.
I don't know why you think that Kashmir is the property of India. It is owned by Kashmiri people only. The majority or minority are within Kashmiri people only, not the whole of India.
The choice now is not for the Kashmiri people to make. Kashmir has made its choice. It is for Indians. Will they let Kashmir get independent from India? Or will the independence of Kashmir occur with fracturing of India into a dozen states? Their choice.