I thought about this awkward moment. After all, the leader herself is pretty introverted, so I was surprised that she would press so hard to get other introverts to stand up in a new crowd. I then thought about how she often runs the session. She recruits others for skits, readings, and other activities on a regular basis. I suddenly realized what she is doing: she is sharing the stage because she herself is uncomfortable there.
Regardless of her intent, it alienated the newcomers and it's likely they won't return. Introverts can be just as insensitive as extroverts sometimes are when they fail to respect others' needs. Self awareness is important. This particular leader apparently was oblivious to how her statements were affecting the guests.
The way to build relationships is not to alienate but to be sympathetic to individual differences. There are plenty of people -- extroverts -- who are willing to stand up and introduce themselves. The way to tell which one you have -- an introvert or an extrovert -- is if you have to prod! Oops -- got an introvert on the line here! We should be even more attuned to our fellow introverts because we know the terrain so well.