My parents think I am socially challenged (figuratively or literally, I am not sure!)?

You're an introvert (as am I), comfortable in social situations but you choose not to be in them. It sounds like you are comfortable with who you are, your parents need to adjust their perspective and realize that you have your own way of doing things that works for you. Ultimately they just want you to be happy and if they are very social people it may be hard for them to understand that you are happy being less social.