Sri Lankans are good people and so are Tamils. But LTTE is a terrorist group that wants to carve out its own state from Sri Lanka, which has always been a Sinhalese Buddhist kingdom. The Sri Lankan government put down this insurrection legitimately.
By contrast, india is an artificial entity of separate hindu kingdoms, one of which is Tamil Nadu. Letting Tamil Nadu go would simply be restoring natural borders. It would not be terrorism or separatism.
Tamils are friendly with Pakistanis too, it seems:
major facepalm, you should change the username to SenileChallenger