Why is avoidance coping not helpful for those with anxiety?

The problem with avoidance coping is that we think to ourselves, "Oh, I went to that place, and I got anxious. So I'm not going to go there again." This causes your world to get smaller and smaller, as people find that there's always something more that needs to be avoided. So what we want to do with any kind of anxiety is to not fall into that trap, and instead, learn that you can go into that situation even if it makes you anxious. Realize that you have the tools to help yourself get through the wave of anxiety and let it pass.