That's one definition, but it doesn't have to be the only one. Lifestyle and education fit just as well under Race or Theme, after all.
Yes, lifestyle and education could be a race or theme. You can make an aristocratic race, class, or theme.
But one of the iconic aspects of D&D is that it is a class based system. A class is a collection of abilities that create an archetype.
Many of the issues with classes was forgeting this or making the collection system incompatible. Some classes were not a big enough collection of aspects (fighter was just weapons and armor for a long time). Other had a too big of a collection (most casters).
Laser focused classes can also be made more akin to skills system if done incorrectly. The higher your Evoker