Although I have social anxiety now I didn't when I became friends with my best friend who is severely social phobic. We met when we were fairly young so I can't say why I became her friend but I always re-assured her that it I who am lucky to have her as a friend (she hardly ever believes it) Also I find now that both of us are socially impaired we try to help each other as much as possible (even when we don't listen to each other)
As for your outgoing friends, they are your friends because although sometimes its hard for us to see ourselves under your insecurities and social anxiety is a truly remarkable person and thats who they see.