I don't believe that introverts are any more inclined to be insecure in social situations than extroverts. The difference is in how they deal with it. Both tend to deal with it from their comfort zone. From my introverted tendency to observe people, I've noticed many an extrovert being loud and obnoxious.
After watching for sometime, I often realize, the person is actually rather insecure and appear to think it is being covered up by being loud and obnoxious. Once I identify what's going on, I tend to ignore the behaviour and to some extent the person. That tends to happen with the introvert who copes by being quiet.
Although, some of those quiet introverts are just very comfortable in their own skin and really see no need to say anything unless they choose to.
I remember observing an individual who was very very quiet and trying to figure a way to help bring the person out of his shell a bit. I stopped that quest the day that he choose to speak up on a subject and did so with great confidence and authority. Was all I could do to not let my jaw drop open.
A certain degree of self-confidence is pretty necessary on both sides of the spectrum.
that is why we cannot talk in absolutes. there are many extroverts way different than the norm, which applies to a lot introverts as well