Kashmir is the most important strategic post bordering 3 nuclear nations at war-ish with each other.

It is landlocked, with each country controlling different parts of it, and 2 claiming it in entirety.

J&K is a 3 part territory, of which 99%+ of Leh, Ladakh and Jammu want to be a part of India. So, if Kashmir was to be independent, it would be tiny, vulnerable and entirely dependent on neighboring states, that it would be at war with.

Now, there is also the fact that over the last 200 years, native Hindu Kashmiri communities have been driven out (literally, by violence) of Kashmir, so Kashmir independence can't exactly be unilateral.

Lastly, India is a proper democratic nation. States have full rights and religious + cultural diversity is celebrated. I am as biased as it gets, but I'd say India is the best option among Pakistan, India and PRC run China.

Depending on what you read, separatism in both places is either fuelled by fundamentalist ideologies or right for self determination. Kashmir is far more tricky though based on how the separatism has been fueled into an armed conflict by a neighbor.

To understand the sentiment in both places, you will need to read the history of both countries, and no it doesn't just start from 1940s.