“This world, Kaccana, is for the most part shackled by engagement, clinging, and adherence. But this one with right view does not become engaged and cling through that engagement and clinging, mental standpoint, adherence, underlying tendency; he does not take a stand about ‘my self.’
-- SN 12.15
My understanding is that identification and possession are adherences, they are clinging. Nirvana, when conceptualized into a "thing" becomes something to possess or to identify with -- which is no different than clinging to any other conceived idea:
“He perceives Nibbāna as Nibbāna. Having perceived Nibbāna as Nibbāna, he conceives himself as Nibbāna, he conceives himself in Nibbāna, he conceives himself apart from Nibbāna, he conceives Nibbāna to be ‘mine,’ he delights in Nibbāna. Why is that? Because he has not fully understood it, I say.
-- MN 1
Such a tendency to hold something as a self is said to be at the root of misunderstandings and a cause of suffering. But Nirvana, rather then a 'thing', is said to be simply a name, a designation for the end of dukkha.
"Bhikkhus, you may well cling to that doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it. But do you see any such doctrine of self, bhikkhus?"
—"No, venerable sir."
—"Good, bhikkhus. I too do not see any doctrine of self that would not arouse sorrow, lamentation, pain, grief, and despair in one who clings to it."
-- MN 22