...I think identity in this context is largely the "I am a" form.
I'm a giggler is identity. I juggle, or even I am the juggler is not the same sort of a mark of Identity. So I'd say the advice is is avoid (or at.least recognize and minimize)) thinking in the "I am a" frame.
I agree the advice in the article is to avoid "I am a ..." but given that seems somewhat impossible and the advice is to avoid this construct in order to prevent a kind of 'dumbness' as described by the article, I was wondering if it would be sufficient to avoid 'non-verb-ifiable' nouns in order to achieve the desired outcome: prevention of dumbness. I should have made that aspect of my comment clearer.
I'm a giggler is identity. I juggle, or even I am the juggler is not the same sort of a mark of Identity. So I'd say the advice is is avoid (or at.least recognize and minimize)) thinking in the "I am a" frame.