For the same reasons you already mentioned! They already have threatened to attack India, they already have kidnapped Indian workers and nurses and we have an interest in a stable middle east, not to mention that even training Iraqis or selling them weapons is reason enough for them against us, if they would need a reason anyway. Terrorists "create" their own reasons and arguments, which don't have to be valid, they only have to sound good in the minds that are open for such BS.
So since we already are involved and we have an interest to stop them to increase their influence in the region and if that's the case we have to take responsibility in actions too. I wouldn't provide ground forces either, but air power, logistics and training, or like the Russians do, sell them 2nd hand fighters.
True, but this is concerns Indians too and the more influence the IS gets in the middle east, the more Indians will be effected, be it in terms of jobs, be it a direct threat to their lifes, India could even be effected by limited oil supply and so on.
Anyway we should stay away from an unwanted attention.