We owe Carl Jung a giant thank you for discovering introversion versus extraversion and beginning the study of personality as a science. Advances make society better over time.
You can certainly poke holes in his vision of personality. For one thing, it's based on a theory of 4 bodily humors that traces back at least to Plato. You know the one—if you're angry that's yellow bile acting up (hence "bilious"); if you're depressed that's your black bile (hence "melancholy"); if you're anxiously careful that's mucous (hence "phlegmatic"); if you're impassioned and impulsive that's blood (hence "sanguine"). Spotting all the threads tying the Myers-Briggs Temperament Index derived a few years later by a mother-daughter team (who still get lambasted in an overly sexist way) to the 4 humors is fun, but I'll leave that to you if you're curious.
What I'll say is that although the bodily fluids idea turned out to be rubbish, the personalities pinned to different bodily fluids still make a good dab of sense. This wasn't half-bad for a first try 2400 years ago. No doubt that's what attracted Jung. Fortunately, he threw out the fluids hypothesis. Aside from "we notice these patterns" and "we hypothesize they arise from these bodily fluids"—before real science existed, I don't think anyone even put it forward as properly as that—there was nothing scientific about Plato's model of personality. It was just some good, informal observation tied to a baseless, untested, and unadmitted hypothesis as to the mechanism. (Actually, I don't think Plato brought in the fluids at all. If I remember correctly, that was Empedocles. So you could say Jung went all the way back to Plato's sketch of personality types, skipping Empedocles and all the medieval and wrong ideas about nutrition and medicine that followed.)
Carl Jung made it a little better. He was a trained experimental and observational scientist. Admittedly I haven't read a single one of his numerous books detailing the baroque framework he devised (personality is indeed complicated), but as a researcher and clinician who took copious notes, he based his ideas on some kind of empirical trail. This is so often forgotten, because it seems also very clear that he had a mild form of psychosis, which contributed to his themes of spiritualism and superstition and his love of mythology.
There's nothing necessarily wrong with that, though. It's how he was. We can still credit him with discoveries he made.
Actually, there's something good about it. He influenced the study of folklore and religion and storytelling tremendously. We can thank him, in part, for popularizing some of the most effective techniques in today's books, tv shows, story-based games, and movies.
My reason for saying this is just that I was standing by the microwave waiting for some chocolate milk to heat up, musing about humans as social creatures. Introversion/extraversion clears up a bit of confusion and helps us get along. There's really a ton more to it—that duality is only square one. But it is a first step to really understanding human socialization: conflict, empathy, cooperation, etc.
In fact, Jung came up with the idea while trying to explain to himself why he had such a big falling out with his mentor, Sigmund Freud. The eventual solution, in his mind, was to see this big divide between their two personality styles: Freud was something Jung decided to call "extraverted" (there are stories about how Freud made endless numbers of friends by memorizing everyone's name and details about their lives, so he could ask good questions if he ever met them in the future) while Jung was "introverted" (at one point in grade school, he was so shy he couldn't even go to class and had to be taught at home for a while). Today we wouldn't see that as a reason two people can't get along. But imagine a world before "introvert" and "extravert" existed as words. How would you understand what Jung struggled to understand about this big clash with someone he loved?
Maybe you wouldn't, and maybe people get along better today because of that fight, and the ideas that grew from it.