Does anyone say he is his body, period?
What is it that makes the body such a scandal? Is it because bodies we see are not our bodies? Is it this un-identity, the fact that empathy seems like a childish dream, some sort of ridiculous belief? Is it that touching is losing my own touch? Listen to Wittgenstein: The truth is: it makes sense to say about other people that they doubt whether I am in pain; but not to say it about myself.
So there is a basic egocentrism in our thinking about the body. In English, we say "take a walk in my shoes". Compare it to the Polish version: "put yourself into my skin". (Strange, how my skin seems to define me.) Is a racer without his car still a racer?
And that's where the fear of skin appears. And the obsession of skin. Its shapes, tones, actions.
How many skins can I have, how distant is this skin from mine, what can be done with this skin. Using it to re-create identity, as a toy, a scandal, or any other pretext. And we all do it - which is scary, and nice : feel the carress. It translates the other into what's yours.
And vice versa.
NB: Here is a short overview of body in contemporary art (in French)