Here are the lines I am talking about,
My point is if Pakistan and China control some territory of Kashmir, why are they keeping those issues dangling for years rather than establishing international borders along those lines?
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Simple answer: Politics
International Border is the line that both countries and the rest of the world have agreed upon. Both LOC and LOAC are unofficial control lines which are taken by the armies.This border is not accepted by either nations as official. India still wants to take back Pakistan-Occupied Kashmir(Or Azad Kashmir as is called in Pakistan) and Aksai Chin while Pakistan wants to take the whole of Jammu and Kashmir and China wants Arunachal Pradesh which it considers to be Southern Tibet.
Now, let's be honest. All 3 countries, being nuclear powers themselves, know that a war in the 21st Century is not possible. Status quo is the only thing that establishes some sort of peace between the countries. However, all 3 countries have to satisfy the nationalistic fervour in their own countries. It has become an emotional issue in the democratic countries. In Indian terms, Kashmir is a "Brahmastara" (Invincible Weapon) for politicians. In either India or Pakistan, if any leader even tries to resolve it, they are just committing political suicide. Because resolving means negotiating and people on both sides of the border want absolute control and no negotiation.
There are many reasons.
Kashmir is used as a political weapon in the countries. Any yield or comprise would be political suicide.
The land occupied by Pakistan and China was occupied by force. If these borders were recognised, The Crimean occupation of Russia, China's occupation of the South China Sea, Houthi insurgency in Yemen, Syrian insurgency, Islamic State, etc. would have legal precedent to be recognised.
There is no point for the recognition and it would not directly benefit any of those countries.
EDIT: For references:
As you can see in both the wars Pakistan and China were the initiators, in fact, the Accession of Kashmir was forced as Kashmir was unable to defend itself, if Pakistan had not started the war, Kashmir may have been independent and this border dispute probably would not have happened.
China has demonstrated its willingness to concede large tracks of land for the sake of peace, but experience has shown that compromise to India does not lead to peace. See Maxwell's This Is India's China War, Round Two. It seems that India has resumed its ancient career as a stooge for its colonial masters. As long as India continues to bite China's kneecap, India can rally massive support from the western world.
The 1962 war was the result of Nehru's decade-long rude encroachment and his not-negotiable attitude. After a decisive Chinese victory Chinese troops declared unilateral ceasefire and withdrew to positions 20 kilometres behind the previous line of control. India, instead of using this opportunity to break contact with China, quickly sent their defeated army to reoccupy every inch of land that was voluntarily evacuated by Chinese troops. Southern Tibet was part of Greater China before India was part of the British Raj and before British Raj there was no such thing called India. Mao ordered the withdrawal on a whim because he was eager to make friends with Indian people and was ready to bestow largesse to his friends; at the back of Mao's head, poor people are natural friends. If India had made the slightest friendly gesture, Mao would have renounced Southern Tibet. Instead of reciprocating China's good will, India mounted accusations after accusations against China and waged a decades-long anti-China propaganda campaign and cultivated a nation of rabid China haters.
For the next 50 years, China's strategic interest along the border was peace, not land, but India used the border issue as a political bargaining chip. Every time China makes a concession (See Sikkim and Souther Tibet), India claims more. Even worse, under the pretext of China threat, India started a new round of nuclear arms race after the cold war when everyone else was in the mood for nuclear disarmament.
As the older generation slowly departed from the scene, China's new generation of policy makers began to re-evaluate the assumptions China previously held about India. If compromise does not work, China today has no other choice but the opposite. India has taught China how to haggle: if you want peace, you have to ask for a lot more. Starting from 2012, China's policy changed from "peace above all" to "whoever makes trouble for us will have to pay for it."
The following was Bertrand Russell's observation of the 1962 conflict:
When populations have been worked up to a pitch of bellicose excitement, it becomes very difficult for governments to restrain them. This has happened most notably in India. The government misled the population by concealing the fact that the Chinese had a legal case which, on the face of it, was as strong as the Indian case, and that what was needed was negotiation supplemented by arbitration if necessary. China was willing to adopt this this course, but India was not, because the Indian government had persuaded Indian public opinion that the Chinese had no case.
Russell, Bertrand. Unarmed Victory. New York: Simon And Schuster, 1963. 143. Print