I'm gonna start off by telling you a little background. I'm the most introverted person ever, I still don't like ordering for myself at a restaurant or answering a question in class. At the same time, I can have a conversation with a chair and not be embarrassed at the fact that I'm literally having a full on conversation with nothing (which I found out at recruitment this past year).
I hate ordering for myself at restaurants or answering questions in class, it's honestly one of the most nerve-wracking things ever. However, I hate not having people to talk to or bounce ideas off of. When you don't include me, it hurts me, but at the same time it's a wave of relief because I don't have to be social. It's literally a constant battle between being super social and staying quiet.
I can't speak for everyone, but it's really hard to not feel left out in a group of people. Yes, I can be the most outgoing, carefree person in my friend group, but I can also be the most quiet and isolated. Have you ever thought that extroverted introverts have been pushed to conform and that's why they have qualities of both? That question may be irrelevant, but also many be super accurate.
If you have a friend like this, here's some advice: don't make them feel alone, push them out of their comfort zone, and let them know you're there for them. Extroverted introverts can honestly be the best friends you'll ever have because we have qualities to help you get going, give you motivation, and listen without butting in.
If you are like this, here's some advice: let yourself be happy and carefree more often, limit your alone time, and always know that you are so special.