I mean, after all, we have First Class..doesn't that make Business class "Second Class" and Economy "Third Class"?

And if there is no Business Class, does that make Economy "Second Class"?

Is it just a marketing thing? Who would want to be reminded that are getting the third and lowest tier service. Calling it "Economy" works much the way it does for cars..to imply a clever frugality. And this applies I think to the retention of "First Class" in the top tier of service, where people who use it DO want to be reminded that they are getting the highest available service.

No matter what you call it, that's what it is though, isn't it?

Train systems in Europe still do this, but airlines so far as I remember phased out the phrases "Third Class" and "Second Class" in the early 60's I think.