Nancy approaches the topic by stressing the singularity of touch.

“That’s what the body is. (...)an inside that feels it is outside—we should say not that this is the property of a subject or of an ego, but that it is the “Subject.” And even “subject” is extremely fragile, since we should say, not that “I,” body, am touched and touch in turn—that I’m sensed—but rather try to say (and this is the whole difficulty) that “I” is a touch. “I” is nothing other than the singularity of a touch, of a touch that is always at once active and passive(...).
“The unity of a body, its singularity, is the unity of a touch, of all the touches (of all the touchings) of this body. And it’s this unity that can make a self, an identity. But it’s not a matter of a self, an identity or a subject as the interior of an exterior. It’s not (...)subjectivity as incommensurable with exteriority, extension, and exposition. No, it’s a matter of a “one,” and a “someone,” of the unity or singularity of what I in effect really want us to keep calling an identity, an ego, a self, a subject, provided that the subjectivity of this subject is clearly understood as a being outside the self, as a “self-sensing,” but as a “self-sensing” that is exactly not a being posed by oneself and an appropriating of oneself to oneself in a pure interiority, but a being in exteriority in relation to itself. We sense ourselves as an outside. This is not just a question of the hands, but basically concerns the sense of existence(...).”--Jean-Luc Nancy, CORPUS, pp. 131-32
 

In practical terms then, the reason people cannot tickle themselves is because their subject cannot disunite itself to really touch its body that way.