I think I'm an introvert, because I find that socializing drains energy. However, I find that spending regular time with others makes me happier overall.

I don't know if that's true for everyone, but there's certainly a correlation between social time and happiness across the population. I suppose that could mean introverts are just naturally doomed to be miserable—but to me, it seems more likely that even introverts benefit from socializing. Maybe not you, most many if not most.