We usually hear that being “authentic” is to “be yourself”, as opposed to “pretending”. But consider some clues about authenticity:

People who believe they’re behaving authentically are less distressed and have higher self-esteem. … Feeling inauthentic in one’s dealings with other people correlates with symptoms of depression. … Women … report much greater feelings of personal authenticity in their romantic relationships than men do, and as teens, they’re more likely than boys to say that they can be themselves with their best friends. On the other hand, teen boys report feeling more authentic with their dads than teen girls do—and young men say they feel more authentic around professors than their female classmates do. … When adults … were asked how authentic they felt in the presence of various people, work colleagues came in dead last. (more)

This clue seems especially telling:

Subjects sometimes reported feeling more authentic when they acted “out of character” during activities in the lab, such as playing Twister or debating medical ethics. Introverts felt “truer to themselves” when they were acting like extroverts; ditto disagreeable people who were acting agreeable, and careless people who were acting conscientiously. (more)

Note that people felt the most “authentic” here when they were less like their usual self! This tempts me to guess that the feeling of authenticity is actually a feeling of being accepted and respected, with an absence of stress about if one is so accepted. So when a personality spectrum has a more respected end, we all feel more authentic when we feel that we look like that end of the spectrum.

This fits the other correlates above; people feel more authentic when they feel more accepted and respected in their role, regardless of if that role is who they “really” are.

Maybe there is no real you. There are just the yous that you can construct, and the you that you can make that seems the most accepted and respected, that is who you prefer to see as the “real” you.