How innocently you are saying 'make LOC a border and live hapily there after'. Hahahahahah .. I am still laughing. This is one of the most intractable and long standing conflicts in the world. Three major wars have been fought over this and thousands and perhaps even more than a million people have died. The result so far is that India controls almost two-thirds of Kashmir and Pakistan controls one-third. China controls the rest. The conflict continues. Most scholars who have studied this issue feel that Pakistan has the stronger case. However, India has more people to advocate their point of view.
When British India was given its independence, India was supposed to be divided into two countries: India and Pakistan. All areas which were more than 70% Muslim were supposed to go into Pakistan. The rest would be India.
However, the "princely states" would be left to decide on their own. They could join either Pakistan or India or they could remain independent.
The rulers of many states were for a time not sure if they wanted to join Pakistan or India. But eventually they joined one or the other with passage of time. But in Kashmir, there was an immediate war. According to the Indians, troublemakers from the Northwest Frontier were causing riots and agitation in Kashmir. As a result, the Maharaja of Kashmir joined India and requested the assistance of the Indian Army. The Indian Army arrived immediately and Pakistan attacked the next day.
During this war Pakistan was about to run over all Kashmir but Indian went to United Nations with a request of Ceasefire. UN passed its famous and historical resolution after declaring ceasefire between the two. This resolution states a plebiscite among people of Kashmir to resolve this issue. When Pakistan built a road to China known as the Karakorum Highway, India protested to the United Nations that a road was being built across "their territory" without their permission.
However, Pakistan has a different stance. According to Pakistan Kashmiri people themselves want to join with Pakistan. The Maharaja of Kashmir had no right to call in the Indian Army. Instead he should ask his own people first. Finally, the agreement was that any areas more than 70% Muslim would go to Pakistan. Kashmir has more than 90% Muslims and therefore clearly should have been part of Pakistan.
Currently every one of these polls has had a similar result. Some want an independent Kashmir. Some want to join Pakistan. Almost none at all want to stay in India. The very few who do want to stay in India are recent arrivals, primarily Hindus, who do not have long heredity links to Kashmir.
Nobody on the Pakistan side of Kashmir wants to join India, but a few would like to have independence.
Kashmiri people feel closer to Pakistan culturally and religiously. Finally, British were at fault for not resolving this issue before pulling out in 1947. And US is making another mistake not resolving this issue before pulling out from this region.