In Dependent Rational Animals, Alsadair MacIntyre says "we are our bodies". In the singular form I can put that as: I am my body (which, unbeknownst to me till about 3 minutes ago, is the title of a book by Elisabeth Moltmann-Wendel). There is a linguistic problem here, however. Namely this: to what does the "my" refer? Surely the thing/being itself -- in this case, the body -- cannot possess itself. A tree, if it could talk, could rightly say "These are my leaves", but it could not say "I am my tree". In the same way, a body cannot say "I am my body".
"I am my body" is in fact a self-refuting statement, because it says that there is something else to which that body belongs - a higher self that can intelligibly say "my body". More accurate, if this is your line of thinking, is to say "I am a body" or "I am this body".
Indeed, if this is true, then perhaps we can't even talk about "my hands" or "my thoughts" (nor can the tree talk about "my leaves"). Hands don't belong to this body, at least not in the same way that the notepad in which I first wrote all this crap down can be called "my notepad". These hands are a part of me - they participate in my being. I am not hands, but neither do I have hands; rather, hands (and other things together) constitute this body.
"My" can of course do different jobs. We can say "my car" and "my God", but the difference in meaning is (or at least ought to be) far greater than God merely being substituted in for car.
I'm not really sure what I'm getting at here, if anything at all. This may be nothing more than pedantry at best or idiocy at worst. Or maybe it's the other way around.
One point to possibly salvage this is the connection between our (over- or mis-)use of "my" and Jesus as non-possessor; non-possessor even of his equality with God. Our identities are too often formed by the amount of things or people we can put after the word "my" (in the possessive sense). Yet if even this body cannot be called "my body" (and St Paul confirms as much when he tells me my body is not actually mine), then what else do I mistakenly think I own or seek to own? Unlike Jesus, we have a tendency to consider everything and everyone as a thing to be grasped. But if divinity itself is not to be grasped, how much more is everything else beyond our reach? Which is another way of asking: what have we got that we did not receive?