To force yourself to reach out, to me, implies that there's something wrong with being an introvert (or wallflower).
I don't like the idea of admitting that such a natural state of being is in any way abnormal or wrong.
It always seems like introverts don't mind being in a world of extroverts, they just find methods to cope. Extroverts, though, seem to view introverts as "weird" or "shy", somehow incomplete shells of a person. At least, that's my experience.
I never see someone trying to make an extrovert more introverted; but I consistently see the opposite.
To answer your question: I do like to reach out, but for different reasons. It seems extroverts want to reach out for the sake of making contact. -- They're OK with just having drinks, games, making small talk, etc.
As an introvert, I'd rather go to get some mental engagement. I'd go because there's something I can learn from the meetup or it's a meetup surrounding an interesting activity.
It's not about being with people. -- It's about what those people represent [cultures, ideas, insight, knowledge].