See, even you recognize that India is supporting separatism in China, since the Tibetan government "in exile" claims to be the true government of Tibet.
Here is something to remember: China has no active armed insurgencies.
Whereas India has too many armed insurgencies to count... the Kashmir insurgency, the Maoist insurgency, the insurgencies in the North East...
India has been supporting the Tibetan government in exile for half a century. Imagine if China started openly supporting Indian separatist groups, your country will be broken into pieces easily.
Just wait till your arrogance causes you to take one step too far.