... in business class, repeatedly claiming that it's first class. Why?
LOL - I have this discussion with my wife repeatedly, where I note that we're flying only business class and she argues that if there is no further forward class available on the flight, then it is [the] first class (see some of my TRs for examples - VA, BR, old US Envoy [no TR], OS, LO, QR [routes w/o first, like on the 787], VS [no TR...yet], DL [no TR ...yet], etc.) and she reminds me that all of those international business classes are waaaay better than domestic "first" class; so, what does it matter what name the airline labels the class? she asks.
I'm still on your side of the debate, though.