This happens because the person feels overwhelmed by the anxiety. Athletes and other performers learn to regulate this anxiety so that they can have just the right amount. If they don't have any they won't perform up to their potential but if they have too much it will interfer with performance. The same is true for you. Learning to keep your anxiety from overwhelming you is the key.
Unchecked anxiety can easily become overwhelming given the right high-pressure situation.
There are a variety of factors that seem to be involved here. A third factor seems to be heredity. It appears that the tendency to experience overwhelming anxiety may run in families. So if you have a parent who struggles with anxiety you may also be prone to the same. Finally, some people are less likely to be affected or overwhelmed by anxiety because they have learned ways to react to, and control, normal anxiety when it arises.