There is but one argument for your position: I could die at any time, in any manner. "But that does not mean one should seek death out!". Ah, but precisely it does. Because death is our utmost, ownmost possibility, and exactly because it is possible at any time in our lives we ought each and every day to seek death out and to try and comprehend its meaning.
But what does it mean, 'to seek death out'? It means to recognize the unique possibility of one's own death in every moment. It means not only to take risks but to embrace that all life is at constant risk of becoming unlife. As a possibility, YOUR death is in a unique position of concreteness, or rather, concrete-ability. For death is a certainty, THE certainty for all living things. Seen this way, it is obvious that death both defines life and 'a life'.
Being towards death allows one to fully live - to understand and appreciate the meaning of the life one is in. Awareness of death is the only route to awareness of life: so fully does death structure a living human's existence.