The whole point of Gen X was, and continues to be, a negation of being forced into Baby Boomerdom against one's will.
Remember travel agents? Remember how they just kind of vanished one day? Well, that's where all the other jobs that once made us middle class are going, to that same magical, class-killing, job-sucking wormhole into which travel agency jobs vanished, never to return.
How can I be a part of the 1960s generation when I don't even remember any of it?
Failure is authentic, and because it's authentic, it's real and genuine, and because of that, it's a pure state of being.
I think that to acknowledge a new generation is to acknowledge some degree of obsolescence in yourself, and that is very hard to do and often comes with undeniable anger.
Discussions of generations only go downhill. There's no point in having them.