Many people are both depending on the setting and situation is what I should've said but I get what your saying.most people aren't both, but there are definitely traits of both people can have for a variety of reasons.
like i'm an extrovert, every personality test i've taken from childhood to now puts me there, but i have "introvert qualities" simply because of my personality and upbringing. i can be selective with who i talk to because i simply don't have patience for bullshyt/dumb people/people i feel aren't worth my time, i also like to recharge alone but that comes from being the only girl and the youngest in my fam (by a big gap)...it was sort of like being an only child, i knew how to be just as happy dolo as with people.
My real point for that post to make it clear that introvert is just a way to shade the fact that most of these people are weirdos. There are legit Introverts but everyone that claims it is not

