I think you are missing a few points here:

a) Loads of people tend to associate themselves with the “class” of their parents. Thus, a lot of self-made people that would would call “rich” would call themselves middle class… out of habit.

b) Location matters a lot. If you earn 80k as a farmer in the middle of nowhere, you’re probably rich. If you earn 80k in New York, The City or San Fran, that places you squarely among the poor, up that to 160k and you can call yourself middle class (i.e. able to afford renting your own place and quality insurances).

c) A lot of the “rich” people you so despise have this tendency to never be the smartest person in the room. Consequently they always think of themselves as average since they try to associate with people that are better than themselves. This also translates in how they view themselves in the social structure (i.e. average, middling, middle class)

I think that boils down the reasoning for 90% of the people that are “rich” but actually call themselves “middle class”.