The song is about the death of the American steel industry in Eastern Pennsylvania in the late 1970s and early 80s; it was released on 1982’s The Nylon Curtain album. It’s told from the perspective of an unemployed mill worker.
In your typical one-industry town (like Allentown), kids would go from high school to work in the mill, where they had the opportunity to be promoted without much formal education. (“Every child had a pretty good shot/To get at least as far as their old man got”) With the closing of the mills, however, those opportunities went away, to be replaced by massive unemployment.
The song is surprisingly anti-union. (“And the union people crawled away”) I’ve always taken the “But something happened on the way to that place/They threw an American flag in our face” lines as an insult to the men who were facing poverty and economic uncertainty, perhaps by the union and the mill owners; patriotism doesn’t mean a whole lot when you live in a depressed area with no good prospects. I don’t think it has anything to do with Vietnam because that’s not what the song is about.
This is just my interpretation, mind. I don’t claim to be able to read Billy Joel’s mind, nor have I read anything about the song. And, for the record, the Allentown/Bethlehem/Easton region is doing much better, now that its economy is a lot more diverse.