I've had that experience. I am good at socializing, especially when I want to. But I generally prefer to do my own thing, people interpret that as being arrogant and/or standoffish.
I don't think it's a bad thing. As long as it isn't extreme. For example, I am an introvert, I enjoy doing solitary things, I love being in my head, coming up with innovative ideas and strategies and planning. But I am an extrovert when it comes to thinking and ideas, I.e I am very assertive and headstrong. There needs to be a balance.
Extraverts depending whether they are sensors, perceivers, feelings, or judgers, will have introverted functions being exhibited in specific areas of their lives. There is a balance.