I don't know if it's a quirk of the Japanese language, the culture, translation, or whatever, but I dislike the way 'extrovert' and 'introvert' are tossed around so much in a way that's incorrect in what they actually mean.
It's always shown in manga that extroverts are the thing to aim for, they have friends - that being an extrovert is all about your ability to socialise.
Introverts on the other hand are often alone and always poor at socialising, frequently being aloof characters that dislike people.
But that's not what extro-/intro-vert means.
All extrovert means is that your social battery recharges when you're around people, and all introvert means is that your social battery recharges when you're alone.
It's got nothing to do with your ability to socialise, or the number of friends you have.
It's not a matter of 'becoming an extrovert' by being outgoing and being in the popular group, you can very well be an introvert that needs their alone time to recharge, but once recharged loves hanging out in big groups and being the soul of the party.
I feel like the terms 'sociable' and 'reserved' are probably much more accurate terms, but I also think that 'extrovert' and 'introvert' have long been cemented into the media, so it's not going to change.
Unfortunately, it has seemed to influence the anime/manga sphere, with introversion often being viewed as negative in the Western community, which is a damn shame. But what can you do?