It comes from perfectionism - how will you look in the eyes of others?
It has nothing to do with how well actually you are prepared or what level you are at or how remarkable your playing is but everything to do with the fear of failure, fear of looking bad in public, fear of getting discovered that you are a fraud.
Now helping others is an emotion you extend away from yourself. You focus making other people happy.
Another factor helps - immersing yourself into situations of controlled risk more often. The more you do it, the stronger you have a feeling that you have what it takes.
I have an improvisation recital tonight which will be based on the Lithuanian dramatic fairy tale Egle Queen of Grass Snakes. My main focus is not on myself, how well I'm prepared, how well I'm going to play, how am I going to look in the eyes of my listeners but on helping people experience and appreciate this fascinating story created live with musical means.
Don't focus on becoming better than others but on helping others become better people. That's all there's to it.