In public speaking, authenticity is important because our degree of comfort is directly related to our degree of authenticity. The more willing we are to be genuine with our expression, the more comfortable we feel with ourselves.
Conversely, our fear and anxiety is locked up in our reluctance to be real with our thoughts and feelings. People who are anxious and uncomfortable in the world are simply not giving themselves permission to be genuine. They somehow believe that it is unacceptable, maybe even dangerous to be real. Often they have had experiences where being real was not allowed or supported, so they have learned to hide or mask their real selves from others.
The habitual behavior of masking authentic feelings and thoughts shows up as stage fright and fear to speak in front of others. This is the reason so many people say fear of public speaking is their number one fear. The tension that gets stirred up at the center of attention is the tension needed to prevent real feelings from being expressed. It is the tension that protects them from being seen for who they are.
When you can drop the mask, you begin to feel free to share your real thoughts, feelings, insights and awareness with others. Only when authenticity is allowed can you truly overcome stage fright.