It's a very common misconception. One I even held myself until recently. The more I thought about it, I realized that while I am introverted, I do like being around people. I'm perfectly happy to be with and socialize with people - as long as I don't have to be the center of attention or life of the party. Interestingly it was a 3 month stint doing full-time remote work that made me realize this.
Luckily when socializing with other introverts, they're generally OK with silence and gaps in the conversation, it's not awkward. And when socializing with extroverts they're happy to dominate the conversation and I'm happy to let them and just listen.