Interestingly, and falsely I now know, my parents gave me the strong impression that tradesmen and the working class could never climb above lower middle class unless they transitioned to management which was then a white collar position. Not explicitly taught, of course, but very close to it. My father still believes that steelworkers are not middle class. By virtue of being steelworkers, regardless of savings, or homeownership status. It confuses me.

He's right.

Here's the thing: class is not the same thing as wealth/poverty. That's why the term "nouveau riche" exists. It is possible for a person of the upper classes to become destitute, or for a poor person to win the lottery. The Starbucks barista working for $9/hr who works a second shift at $8/hr to attempt to keep a roof over her and her two kids' heads over in Chelsea is not in the same social class as the Starbucks barista working for $9/hr standing next to her, who is there to supplement her crummy TA-ship while she works on her dissertation.

I'm not saying that class varies entirely freely from how wealthy/poor someone is. Generally, class goes up with wealth -- or more accurately, wealth goes up with class, because the things that move you up in class (as it were) pay dividends.