The above is a question that I dance around all the time. Well, "dance" probably isn't the right word, because in reality I do act extroverted, all the time as a matter of fact. Still, there are times when I think about getting more militant about the whole subject, well at least in my own "introverted personal thought bubble" kind of way.
Yes, just because I can stand up in front of groups of folks I mostly don't know...and do it, based on the feedback I have received for a very long time, reasonably well...doesn't mean that I actually enjoy doing it. I claim far less ability in one area where extroverts excel, namely that of "small talk". Words like "awkward", "uncomfortable", and "forced" come to mind just about any time I have to engage in casual conversations with people I really don't know. I can do it, but then again I can also get through a colonoscopy, but that doesn't mean that I want to engage in either at regular intervals.
Another area where I can get somewhat militant in my thinking is that of "collaboration". Yes enjoying collaboration is, to the business world, what loving puppies and kittens is to the world of pre-teen girls. I can collaborate in a group very effectively with others, but it takes a significant amount of extra effort on my part. This is because I feel an inherent pressure to talk to many others (not just a single person, which would be far easier), almost as if I was in a social situation. I guess group collaboration is, in a way, a social situation. Anyway, I watched a terrific TED Talk on the subject of introversion last week, one that also touches on introversion and collaboration.
I never really understood why I get so high-strung when working in a group until I watched this & saw just how stressful this kind of thing can be for an introvert.