The fact is that many of those middle class people are now poor but just don't want to accept it.
I'd always define myself as working class because while I have a STEM Masters degree I am entirely dependent upon my salary (which isn't that high, we don't have US level salaries in tech here in Southern Europe) and I have no other sources of income or wealth (real estate, investments etc.)
I think the insistence of many people that they aren't "working class" is bad as it prevents them from seeing what is really in their best interests.