Because, unlike the rest of the princely states, Kashmir decided to be stand alone and not be part of either one of the independent countries.

Jammu and Kashmir was a majority Muslim state but the King was a Hindu.

Even though it was made very clear from the beginning that states had 3 choices, that was, to join India, to join Pakistan or be independent.

So here's the dilemma.

Pakistan says, they were cheated, as it was decided, majority muslim states would be given to Pakistan and Hindu state to India, as JK was a majority Muslim state it belongs to muslim (but again, states were also allowed the 3 options stated above) Hence chose to be independent.

Now, felt cheated, Pakistan tried to get matters in their own hand and started militant insurgency to gain the control of Jammu and Kashmir.

The fear of losing the land as JK wasn't capable of fighting Pakistan, the then king of JK asked to India to help, and was helped on one condition that, JK would be acceded to India in order to help. And he legally signed the instrument of accession.

Now, Pakistan says, we want Kashmir cause it's rightfully ours Meanwhile India says we've legal rights on JK.