The social norm derives from the expectation that at a certain age a person must make a major shift from a dependent level of responsibility to a distinctly different adult level. (This much should be obvious.)
Pinning it to a specific age is largely an artifact of tradition, though, and a simplification. At 18, you're legally an adult, and often moving away to college. (Most schools require even local freshmen to stay in the dorms.) At 22, you may be a college graduate with the potential to earn enough income to support yourself fully. Note that neither of these have anything to do with the age: they're entirely dependent on how that time was spent.
Not everyone is equally prepared after high school or even after college, though, and moving out on their own may not be the best choice. In many places or family circumstances it simply isn't economically feasible. In fact, it's not terribly uncommon for people to move back in with their parents after some years on their own, whether working or in college. (I know, I'm one of them.) For many here, you may not have graduated from high school or college or be able to earn a decent income.
The fear with children staying at home, though, is that they'll avoid adult responsibilities and place an excessive burden on their parents. Now, it's entirely possible to avoid some adult responsibilities even living on your own, but it can quickly become the path of least resistance when living with people who've already shielded you from adult responsibilities for decades. Prolonged adolescence is a bad thing for everybody involved.
(By the way, this is a common enough phenomenon to have a plethora of names: NEETs, parasite singles, Twixters, the Boomerang Generation, Freeters, etc.)
So, the real answer is that it isn't about age: it's about how much of the responsibility for your own life you're taking on. That in turn depends heavily on one's individual circumstances and their relationship with their parents.
