Anxiety disorders resolve over time.
The reason this is a myth is because anxiety disorders are based in beliefs, and a belief will stay the same until it is changed. Time alone is not the answer. Time allows for opportunity to correct inaccurate beliefs, but without the correction the beliefs and the resulting anxiety disorder will last indefinitely. Some beliefs are easier than others to change. What I look for most is a person who is willing to consider the notion that their belief is inaccurate, and they are ready to implement strategies for change.
Anxiety disorders can be treated and many time can be completely cured. Hope is out there!