Kashmir, as per Pakistan, is a disputed country.
Therefore, if there is a part of Kashmir that is vacant and which is rightfully Indians, as per India's point of view, how is it that India started the show?
There is nothing about India being stubborn. Just because India beat Pakistan to the draw, it doesn't mean that the action was wrong. If Pakistan occupied it before India, would you then say that it was a wrong action?
One could even argue, given your slant of argument, Pakistan should quit Kashmir, since she started it!
Obviously, the logic is flawed, when observing with the background of the issue.
If you understood military operations in High Altitude, you would realise why the Indian Army is not keen to quit the heights.
Ask a military person to explain it to you.