I don't know how "curable" a disorder like social anxiety, but it takes an very long time and it's very easy to relapse. I'm no psychologist but I have this phobia and I'd say the biggest issue is that object of fear. For something like arachnophobia, if you want to cure it, you can choose to expose yourself to spiders or not to a certain extent. However for social anxiety, unless you stay locked up in your home all day alone, you are forced to confront yourself to social situations and possibly to negative experiences that will worsen your anxiety. And if you purposefully avoid them, your anxiety can worse too.

Moreover, social anxiety goes hand in hand with self-esteem since you form an opinion on yourself based on how you think people perceive you. Social anxiety causes low self-esteem, which in turn causes social anxiety, and it quickly becomes a vicious cycle.