Logically, rejection causes us no harm. But emotionally, rejection can be a punishing experience. To understand this, we must look at the ancient environment for which we were designed.
In a tribal group, there will be some small number of available women of breeding age. When a man approaches one, he risks rejection, and if that happens, all the other women will know, which will diminish his value in their eyes - maybe to the point where none of the women will mate with him. This is called preselection - women look for social validation of their choices. A suitor who is preselected will be more attractive, whereas a man who has been rejected will be less so.
Another factor regarding approach anxiety is the possibility that she may already be taken, in which case there is a component of real, physical danger to any male who approaches her.
For all these reasons and more, men are naturally selected to experience approach anxiety. Logically, of course, modern society fixes these problems. If I am rejected, I can simply go to another part of the bar, or leave the bar entirely. I will probably never see any of those people again. But my emotions don't know that. My emotions are trying to do what's best for me.
So how can you avoid rejection?
The answer is: you can't. It isn't the solution to avoid being vulnerable. Rather, the solution is to embrace your vulnerability, to embrace rejection, and let the Field show you what is good and what is bad. Most approach anxiety is a result of imagined rejections, not real ones. Eventually, time in the Field will desensitize you to the emotion of rejection. In a game where you might play five or ten sets every night, losing a few of them here and there never really seems like a big deal.