I have found that being afraid of failure or rejection can both be only a symptom of something else - fear of success.

Striving for any type of accomplishment may carry the dread of not getting there or being laughed at for getting there. It also, however, carries the dread of not being up to the challenges that follow said success. We are comfortable doing things that we are prepared for and accustomed to, but not so much being out in the open and certainly not investing a lot of energy into being out in the open.

Put differently, I think that we often are afraid of failing our challenges; But actual anxiety, the one that sits below the surface and sabotages you against your will, often stems from the dread of failing future challenges. A known and anticipated failure now is less painful than an unknown, but certainly bigger failure in the future.