Original post by India4everNo , the story is much more complex and options are tricky (all I have mentioned can be tracked with any international source)
1. India actually did not had any interest in Kashmir during independence, so it let it be as a separate country. Trouble started when Pakistan army started invading Kashmir with local terrorists , to overthrow the Hindu ruler and conquer the land. The king asked India for help, but Kashmir not being a part of India , it was not possible to send huge army and maintain a constant watch over another land . Thus the treaty was signed to keep Pakistan away.
Pakistan do not care for kashmiri people, it does not even care for its own. Their main motive was to occupy more land and resources of Kashmir. If pakistan any a fraction of remorse for kashmiri people then they would have not send terrorist , who kill every one to cause tension.
If one beg to differ that Pakistan did no such thing , then let me remind you Pakistan army has never won a single war against any country.
So when Indian army arrived , it first stopped Pakistan army from invading any further and took care of local terrorists.
Also the fact that India won four out of four battles with Pakistan , in which three, Pakistan lost so badly that with force alone India could have taken entire Kashmir back and much more. But due to internal (to maintain peace) and external (us , uk etc) pressure India did no such thing.
The line, where the war was fought became the cease fire in 3rd war and LOC in forth.
2. Kashmiri people have no interest in India and still want to remain independent, if could. Pakistan claim to Kashmir due to religion is very hollow. During the first war, Indian army struggled a lot with local terrorist and later with Pakistan sending or funding more terrorist till date, there is still some tension between Indian army and kashmiri's though much less now.
But in starting when tension was high , Pakistan and other group tried hard to show as if, India a Hindu majority country was being cruel to Muslim population of Kashmir, which was a stupid in its self, cause India is a secular country and had more Muslim population then Pakistan.
Till date some portion of pakistani population is under the same hoax of India being cruel to Muslims or that our constitution is anti Muslim which is false , also Kashmir does not follow Indian constitution, but India do regulate on human right issue in a consultative manner with Kashmir government.
Though even in worst situation there was never even a quarter agreement to join Pakistan, let alone a majority.
(Turning a nation into secular was not a day work , it took time ).
3. Segregation was never an option, specially with history with Pakistan.
During the segregation between India and Pakistan , where India became a secular country , Pakistan was a Muslim country .
India welcomed Muslim and Hindu people from Pakistan side during separation , even allotted them land , as red land (fertile) .. Though it was not anywhere enough for the huge losses these people have suffered.
But on pakistan side a blood war had started where hindus and other non Muslim, where thrown out, and put with death warnings by military.
India has no interest to see the same with kashmir with 15+ % non muslim population at that time. Other close regions with Hindu majority would also suffer from the same.
4. Kashmir now means different things for India and Pakistan.
For India it is a liability, because it covers a huge north portion in such a way , that if lost to Pakistan or china , it would have to spend much more in defence, since border would increase and from two side , west and north .
So economically a bad deal.
Pakistan
Kashmir has been seen as a soft target by Pakistan, as it blames every internal problem over it .
It also used to justify its out of proportion large army.
Terrorist in Pakistan also pressure on it, cause it will be a huge gate way to eastern countries like , Nepal , Bhutan etc.
5. Why take Hyderabad ? It was a silly issue where a king alone was being selfish trying to be in power.
Difference here was , people actually did not wanted to be independent and join India, unlike Kashmir who never had any intention to join Pakistan .
Also an example where India have shown proof for being not being Hippocratic is Bhutan and Nepal . With similar situation we allowed these to slit out cause we shared their border with china.
6. Pakistan is 12 on failed nation , while India is 76 th.
Who in the world (except pakistan ) thinks Kashmiri people want to join Pakistan.
7.In the 22 years since the Kashmir insurgency started, Indian economy has boomed while Pakistan economy has gone down the toilet
8.After Kashmir they will ask for Delhi , then UP then somebody will ask for separate Khalistan , separate Nagaland , separate Tamil Eelam etc...