"Haven't even begun to work yet"? So 13-15 years isn't working yet? Those just barely starting out are having to deal with the lowest minimum wage in decades, and social mobility is at its worst since the great depression.
Lower household size can be attributed to more than people moving out. There's far more apartment complexes than ever, far more young people living in apartments. Millenials are buying homes years later than the past averages, and lower household size also is attributed to lower birth rates. Lower household size takes into account MANY factors. More young people are living at home than they have in a long time. And those who are living on their own are doing so in rented apartments, not owned homes like was the past trends.This is one stat among many - the overall trend is a decrease in household size, not an increase.