I have had a few occasions in my life where particular people (who have no RPG experience nor intention to play) were offended at the fact that several people in our roleplaying group would be uncomfortable with an audience during their games.
In particular the one that I worry about the most is a brother, who, after me asking if he had any problems with my group playing in the livingroom a saturday night (walking through and all would be fine, just not taking a seat there, or starting to play the guitar, etc.), he got quite upset because we were "grown up" and we shouldn't really feel self-conscious, to which I answered that we have several introverts who just couldn't help it and have their immersion ruined. I have also tried telling him that it's a very private hobby where you act out a character and it tends to get very personal (we do like our roleplaying), where people tend to prefer to stay with people they trust.
For information, I am 26 years old and my brother is 29. He's an extremely extroverted person.
So, having the context laid out, how do I convince my brother that we're not just being jerks, that roleplaying isn't like any other hobby and that there's a reason we try to avoid an audience?