Authenticity is important because now, authenticity determines your moral worth. Authenticity is the degree to which your present life is in accordance with your internal moral compass. "Are you being true to yourself?" is the central question. 


Before, an external moral framework determined one's moral worth and if you didn't deviate from it, then you were okay. No need to worry about whether it was the right framework or not because it was assumed that was the only framework (traditionalism: family, country, God). But presently, moral identity is a problem because it is not given: it is self-generated. Authenticity and self-fulfillment represent an ongoing pursuit, and there is constant anxiety from the knowledge that this pursuit can go off-course at any time.