The American use of the phrase "middle class" to mean "middle income" is very confusing.
"Middle class" was originally defined by what it was not: There was the aristocracy, who were in charge of other people's lives, owned land, and employed (or owned) people to work that land, who made plans and decisions on behalf of, or dictating the behaviours of, other people; And then there was the working class, who did the physical labour, growing crops, tending livestock, weaving, building, digging ditches, etc.
If you were not in either class; If you employed nobody other than a handful of personal servants (employees who cost you money, but didn't make you money); And yet you didn't have to do physical labour in order to survive and even prosper, then you were in between the lords and the labourers; Between the Upper Class and the Working Class - ie you were of the Middle Class.
Which class a person belongs to is not determined by his income, but by his means of obtaining that income.
The American debate about who is "middle class" seems to be more about dividing the middle class itself, into parts based on income. America's aristocratic class is small and tends (since the War of Independence) to be fairly shy, preferring to pretend, as far as possible, to be middle class; While her working class is, today, mostly either Mexican or black, with the few exceptions being, again, keen to pretend that they too are middle class (despite having calloused hands, and dirt under their fingernails).
The middle class in America today is almost everyone in America today. And not just in America; Most OECD nations are completely dominated (in population terms) by their middle classes. Labourers are scarce, and aristocrats even more so.
So, it certainly makes a lot of sense to discuss social strata within the middle class, in terms of income (albeit with the ongoing necessity to define what criteria are employed, and to read the definitions that are provided). But it's horribly confusing to say "middle class", when what you mean is "middle income". These are not synonymous.