Other comments have mentioned culture, individualism, etc. The society as a whole expects you to portray freedom and success. Financial, responsibility, mobility, and we're pretty selfish even to our family. I'd say, yes living with your parents as an adult is a negative stereotype, there's a stigma to it deep enough that most people just WANT to leave the nest. They also want freedom from their parents/rules/etc so they really just build an urge to leave the home through their teen years. I personally feel like american teens have a ton of rules and limitations. Not sure how it compares to other cultures, but I feel it's getting worse in the US and fear is a big driver IMO.

Parents can be rather selfish too, most can't wait until their kids turn 18 and leave the house. The want to live alone too. We like our personal space. It's common complaint for us Americans when non-USer's stand too close to us or otherwise invade our space. This is a common issue we encounter when standing in line at a store and the other patrons get too close to us. It makes us very uncomfortable and irritated. (This is a generalization of course, but I've had this conversation with dozens of people... it's a thing).