Seems like the English language is designed to keep us in the comfortable cocoon of dualism, the idea that a person is essentially an immaterial soul that "possesses" a body and a mind. So "my leg," "my thoughts," "these eyes of mine," and so forth. We can even happily talk about "my soul" and "my essence" with hardly a qualm about, just whose soul/essence we might be talking about. Note that we differentiate between animate and inanimate parts-"The dog bit my (or your, or his, or the horse's) leg, but not, usually, "The dog bit the table leg."
It's gets even squirlier when talking about so-called out of body experiences. "During the procedure, I saw my body on the operating table."