The term "extroverted introvert" is a confusing one. While some people normally categorize themselves as one or the other, some of us happen to fall into the category of both!
You choose who to be open around.
Sometimes, being around strangers is an agonizing experience. Having to answer to small talk is unenjoyable, and unless you have something lengthy and in depth to talk about, you'd most likely rather disappear. When you're around your close friends and family, you're probably one of the loudest and most talkative in the group.
Sometimes we don't want to go out.
There are some weekends where staying in and watching Netflix, hidden away from the world, seems more enjoyable than going to a loud party where you're forced to socialize with people. It doesn't mean we don't like going out, but the alone time is sometimes nice and well needed.
Friendships are sometimes difficult.
Making friends isn't necessarily hard for us, but maintaining them can be quite the task. There are times when we just don't feel like texting people or leaving the house to make plans. It doesn't mean that we don't want to be friends with people, but sometimes it requires more energy than we have.
Just because we like being alone, doesn't mean we like being lonely.
Alone time is essential in order for us to recharge our batteries. We enjoy being able to do our own thing by ourself occasionally but we also like to be around people who will always be there for us. Being lonely is depressing and not what we want.
You're usually quiet in groups as opposed to one on one.
In a group, you're more of the observer as opposed to the one constantly interjecting. To you, it's more enjoyable to listen and observe. One on one conversations are usually easier for us, although maybe a little awkward at first.