It's all pretty murky. For much of American history, a large percentage of native citizens have always been hostile to immigrants, i.e., the working class. This idea that Americans, regardless of class, just love immigrants who are willing to undercut the value of their labor is a fabrication of American capitalists. A rising tide does not lift all boats here.
Yes, it was drilled into your head. It was the carrot on the stick that keeps people moving.
With a ballooning national debt, worsening social blights, and an objectively bleaker economic outlook, I think it's finally time to admit that the carrot was never there--for the majority of us, and perhaps all of us if the nukes start flying.
It's "sickening" because it's a lie used to keep people thinking about a hopeful future that probably won't exist. If we didn't have this lie hanging over our heads, if we weren't chasing imaginary future rewards, we would demand equitable conditions now instead of continuing to chase after illusions.