Being an extroverted introvert can be exhausting. Being around people often causes social anxieties, but being alone is depressing, Its difficult to balance the two.
Not all introverts enjoy always being alone and isolated. Extroverted introverts like to be surrounded by [small] crowds and we even enjoy talking to people sometimes, we just wont initiate the conversation. One on one conversations are usually favorable, we will sit and chat for hours with you if we don't have to make it a group discussion.
We like to go out and do fun things, but we need time to plan for social events. If you spring plans on us last minute we probably wont want to go if we planned on staying home alone all day . Socializing is a lot of work and it takes mental preparation for us. We don't really care for small talk, it takes too much effort and energy to find things to talk about, so when we are done we will want to relax and be quiet.
Alone time is a necessity, but not too much of it. We get lonely too. Sometimes all we want is someone to sit with us in silence. Whether we are watching tv, or reading different books, company can be nice when we don't have to talk.
Making friends can be difficult. Because we prefer one on one interaction, we never really feel like we fit into a group. This might make us seem snobby for picking and choosing a select few friends, but thats not the intention. Its not that we don't enjoy everyone in your group, we just prefer not to be around you all at once. A few personal relationships are much more meaningful to us than having a large number of acquaintances.
Believe it or not, we like attention, but not if we are put on the spot. Its always nice to be acknowledged for success, but too much hype isn't appreciated. We want our hard work to be noticed, but the thought of being the center of attention, or having to walk up on stage to receive an award is beyond nerve wracking.
Being an extroverted introvert is a challenge. We aren't often understood because our personality is a contradiction, but we understand all sides and just do our own thing, so thats ok.