1. Kashmir was already Independent in 1947.
Pakistan and India invaded it. India could have helped to protect Kashmiri Sovereignty from invading Pakistanis. Instead India blackmailed the Dogra King to join the Indian Union.
2. India promised a Plebiscite and then reneged on its promise.
There really is no excuse for this. Pakistan is more than willing to withdraw its forces from POK, if India did so from IHK. There is even a UN mission (UNMOGIP) established specifically to monitor troop positions in Kashmir.
3. The Betrayal of 1953.
India betrayed Kashmir in 1953 by going back on many of the terms of the 1948 accession. Karan Singh (son of Maharajah Hari Singh, an Indian puppet and even today a Congress leader) dismissed Sheikh Abdullah, the Prime Minister of Kashmir, without allowing him the opportunity to prove his majority in the assembly. The Sheikh will spend the next 11 years in Jail (till 1964), 3 years (1965-1968) under house arrest and another 18 months (1970-71) exiled in South India (Kodaikanal).
4. India makes cunning deals with two Kashmiri families; never with the people.
India's involvement with Kashmir is mostly through deals with two families, Maharajah Hari Singh family or the Abdullah family. Never with the people of Kashmir. There is no reason to believe Kashmiris supported Hari Singh's decision to accede to India or Sheikh Abdullah's decision (in 1974 after 15 years spent in jails) to drop the Plebiscite demand.
5. India continuously rigged elections in Kashmir until 2002.
Or didn't conduct elections at all. When separatists contested elections, India rigged the polls to defeat them. India also claims that separatists who contest elections under the Indian constitution are accepting Kashmir's accession to India! Worse, India even claims that people merely voting in the elections, is evidence of their accession to India. Most Kashmiris reject this assertion.
6. Kashmiri Pandits are ... well, Kashmiris.
Pandits are a very small minority community who don't necessarily support the Kashmiri freedom struggle. They were harmed by predominantly non-Kashmiri militants from Pakistan. Some Kashmiri's did try to save Pandits from the militants. Nevertheless, the Kashmiri civil society will have to do more to accommodate the interests of Pandits. And these Pandits can very well vote (from refugee camps in Jammu or Delhi) to keep Kashmir within the Indian Union, if they want to.
7. Human Rights violations.
Almost every government or human rights organization in the world has called out India for gross human rights violations in Kashmir. Even Indian media report staged killings, fake encounters, disappearances and custodial murders by the Army, CRPF and the erstwhile STF of the J&K police. While some misdemeanor by Armed forces is expected in any conflict, India has provisions like AFSPA which give the Armed forces unlimited powers (and near complete judicial immunity) to harass the civilians. 7 Indian states are currently under such Military rule.
8. India doesn't trust Kashmiri Police.
Why isn't India allowing Kashmiris to police themselves? Militancy that raged since 1989 mostly stopped in 2002. Why are so many outsiders (Army/CRPF) still there? One possible explanation is that India doesn't trust Kashmiris to make a strong police force out of them. And India offers to train the Afghan Army!
9. There are precedents - East Timor, Eastern Europe
Independence movements are not old history book stuff. There are contemporary examples of Republics letting some of their citizens to form separate states. Indonesian occupation of East Timor is remarkably similar to that of Kashmir.
10. Indian Republic is not a Kashmiri concern.
The argument that Indian Republic will fall apart or get balkanized if we let Kashmir go, doesn't wash. India's failures to protect the liberty of people in the North-East is not really a Kashmiri concern. Its India which has to sort out the mess. I support referendums to resolve such issues as Nagalim or Telangana too.
And finally, a part of me wishes that Kashmiris will vote to stay in the Indian Union instead of choosing Independence (most likely) or merger with Pakistan. But its Kashmiris who have to decide for themselves.
A place where the will of the people isn't reflected in the Union or its Government is neither a Republic nor a Democracy.
ps 1: I have deliberately used the word Kashmir instead of Jammu and Kashmir. In general, Kashmir refers to the Kashmiri speaking regions, Kashmir Valley, the surrounding mountains and POK.
ps 2: The people in the plains of Jammu, plains of POK, rugged hills of Gilgit-Baltistan (extending to Siachin and Kargil) and the Ladakh plateau will also have to vote in the referendum for Kashmiri Independence. Hence all these regions will first have to vote in a referendum to formally dismantle the J&K state. Only if they want to, ofcourse.