I and, I believe, most scholars who have studied this issue feel that Pakistan has the stronger case. However, India has more people and therefore more who advocate their point of view.
I have never read a cogent, logical explanation from anybody taking the Indian side until I received a letter from somebody in India a few days ago. Therefore, I have decided to post my view and his view and ask readers to write me their opinions.
Briefly stated, 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 suppose to go into Pakistan. The rest would be India.
However, the "princely states" would be left to decide on their own. They could join Pakistan or India or they could remain independent.
The way I am directly concerned with this issue is that my wife was from the Princely State of Chitral, which is in the extreme Northwest corner of what is now Pakistan. The rulers of Chitral were for a time not sure if they wanted to join Pakistan or India. Eventually, they came to be considered part of Pakistan, but retained their autonomy. The princes continued to rule. However, on January 1, 1971, the rule by the Prince of Chitral was abolished by the Government of Pakistan. This was a popular move, as the long suffering people of Chitral had gotten fed up with their princes. The princes were not entirely unhappy either, because they were given some money and minor positions in the Government of Pakistan. The Prince of Chitral is still in the Foreign Service of Pakistan to this day. Older people in Chitral still say "I am going to Pakistan" when they are going there.
Although the matter of Chitral was resolved peacefully, in neighboring Kashmir, there was immediate war.
According to the Indians, Pathan troublemakers from the Northwest Frontier (places like Chitral and Peshawar) 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, the same day, and Pakistan attacked the next day.
Thus, according to the Indians, India has the right to all of Kashmir. When Pakistan built a road to China known as the Karakorum Highway, India protested to the United Nations and everywhere else that a road was being built across "their territory" without their permission.
However, Pakistan has a different view. The "Pathan agitators" were not from Peshawar. Rather, they were local Kashmiris who did not want to be part of India. Furthermore, the Maharaja of Kashmir had no right to call in the Indian Army, because the Maharaja of Kashmir was not a heredity ruler. He was merely a British appointee. There had been no such position as the "Maharaja of Kashmir" prior to British rule. 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.
The main reason why I and most others take the Pakistan side is that numerous polls have been taken of the people of Indian Kashmir. Every one of these polls has had a similar result. Some want an independent Kashmir. Some (usually slightly fewer) want to join Pakistan. Almost none at all want to stay in India. The 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.
Such matters are often determined by economics. Pakistan has a much higher standard of living and the people are financially better off there than they are in India.
Finally, I must add that the British were at fault for not resolving this issue before pulling out in 1947.