You become an adult at the point you have a significant (meaning, major life impact) responsibility to at least one other person.

That can come from (examples):

1. Becoming a parent (most people) 2. Becoming an employer (who's employees depend on you and the business for their livelyhood) 3. Other examples that you can come up with

At the point that your actions, decisions, the way you present yourself, how you spend money, etc have consequences for more than just you is the point where you really grow up.

When it's all about you, you don't really have responsibilities you just have stuff to do.