This is a profound misunderstanding of introversion. An introvert may choose to develop and use the skills of social connection that come naturally to an extrovert. But at what cost? If the situation demands extroverted behavior, then do it, fine. But the introvert pays a cost to recharge and come back to whatever equilibrium is normal for them. If the cost/benefit does not work out, an introvert can and should make the choice to exhibit introverted behaviors.
Being an introvert who is capable of extroverted behaviors, I always felt confused about the question, "Are you an introvert or an extrovert?" It became clear to me when I read an explanation that went like this: After a dinner party where you meet some new people are you left energized or exhausted? If you're exhausted it is because you're an introvert.
My issue is it just so greatly depends. Certain parties, if I have some sort of pressure on me, I leave tired. Other parties, I leave happy and contented. I might even be tired, but overall happy! When I'm going to a party, I might feel dread, or I might feel exhilarated! And that rarely has an impact on how I feel after the party/gathering.
That's largely why I think the introvert/extrovert theory is not super accurate as a theory. In my experience, my energy after a party is not a constant that depends only on my personality. It depends almost entirely on external factors -- what my day was like, where my head is, who I'm meeting, what they're like, what we're doing, etc.
And: I can often place myself in a state of mind that makes me more or less amenable to a social gathering, and helps me enjoy it more; which will generally make me feel less tired/more satisfied when I leave.
Being an introvert who is capable of extroverted behaviors, I always felt confused about the question, "Are you an introvert or an extrovert?" It became clear to me when I read an explanation that went like this: After a dinner party where you meet some new people are you left energized or exhausted? If you're exhausted it is because you're an introvert.