Its mortality. Their mortality.
Like everyone I think that I must be different, not like the others that are going to die, but I know I am not.
Heidegger talks about how Dasein is immersed in the Mitsein, The They. It is when Dasein orients toward its own death, which will totalize its life, that it becomes authentic.
So between my mortality and their mortality is the possibility of delusion, or authenticity according to Heidegger.
Of course, Adorno wrote the Jargon of Authenticity deconstructing this idea of Heideggers.
One very interesting book about the body is S. Todes Body and World http://en.wikipedia.org/wiki/Samuel_Todes