If the unexamined life is not worth living, why not?
The unexamined life is a life where a person is carried along by their appetites and their caregivers, internalizing the values others teach that person through their need for food, shelter, safety, a sense of purpose, and a sense of social connection.
The unexamined life is not worth living because it ignores the deeper-but-less-immediate human needs:
1) to examine reality as perceived by that particular individual,
2) to examine an individual's own ability to make a valuable contribution based on the individual's own perception of self and of the rest of reality,
3) to examine dissonance between one's own perceptions and the perceptions of others,
4) to adjust course and adjust world view based on ongoing perceptions,
5) to build and affect a shared sense of reality (a social construct) with the circles of friends, family, acquaintances, and larger society around an individual,
6) to imagine the best world possible and to take steps to leave the world more like that for future generations.
The funny thing about those who do a good job at meeting those needs individually is that they often leave a culture that teaches the group to suppress and penalize those who question the latest social construct.
So, to build a healthy social construct, a person must deliberately teach oneself and those impacted by oneself to think for themselves and to question everything.
Think for yourself.