We are born into a world in which our family, physical realities, social structures, etc. shape our identities. To accept this without a second thought is to live inauthentically. Those who critically about the way our identities are shaped by our reality take the first step to living more authentically. Although some inauthenticity is unavoidable, those who think most critically about their existential situation will be more able to choose their own identities.
Heidegger thought that one who thinks critically about existence engaged in existential anxiety ("angst" in his writings) and this comes from the project of accepting responsibility for choosing one's own identity. That is, people tend to go about their daily lives without questioning everything. The authentic human entity begins this questioning, and in doing so is face with the anxiety of questioning his/her own Being (Dasein). For Heidegger, one must accept that he/she is essentially a "being-in-the-world." And to accept responsibility for one's own identity, to be authentic, one must accept mortality: "being towards death." In accepting a "being towards death" attitude, a person accepts responsibility by accepting this individual fate. No one can die for another person; therefore each person is, in this sense, responsible for his/her own death. Accepting the inevitability of death, a human entity is less likely to procrastinate and more likely to actively engage in critical analysis of life; more likely to pursue a more authentic life.
Choosing to move from a generalized "they-self" to a more individually responsible "Being-one's-Self" is:
deciding for a potentiality-for-Being, and making this decision from one's own Self. In choosing to make this choice, Dasein makes possible, first and foremost, its authentic potentiality-for-Being.
(Heidegger tends to use terms like "human entity" instead of pronouns or terms like "subject" because he thinks terms such as these are philosophically misleading.) The human entity's 'existence' ("Dasein") is made authentic if that human questions tradition thereby opening new possibilities. This authenticity of questioning cultural and social traditions (as well as questioning the history of philosophy) is seen by some theorists as an influence on the postmodernist critique of metanarratives. Heidegger's proposed "destruction" of the history of philosophy was a precursor and influence on deconstruction, particularly in the work of Jacques Derrida.