Part of this is true, in terms of inflated expectations and unsupported self-esteem. Adults encouraged those problems, but it's mostly the kids who bought into them.
However. The parts nobody wants to look at is where the adults really fucked things up in ways the kids couldn't easily fix just by disbelieving a bunch of baloney.
1) The economy is a complete and utter wreck. Everyone who is not rich has been gutted. America is a much, much worse place to look for a job now. The jobs are mostly shit with shit pay and few if any benefits. People spend so much time scrabbling to survive, there is no time or energy left to have a life. Nobody would be happy with that, even if they tolerate it. The number of people who can claw their way to the top of that bucket of crabs is tiny.
2) The rest of the social structure is far more fragmented than it used to be. Smaller, more broken families; less church involvement; less secure employment; more moving around; these all fracture the bonds that used to support people through difficult times. So that makes it harder to cope. It is also hard to fix when almost nobody has a complete set of social skills anymore; even if they're willing to do the work, they don't have the tools. It is possible to use self-help and counseling to get the tools, if you have lots of free time, energy, and money. It is about as hard as building an entire toolbox of hammers and wrenches by hand.
3) "Nobody is special" is bullshit. Everyone has their own unique set of strengths and weaknesses. Where adults completely fell down on the job was helping children identify what they are good at and enjoy doing. That's what you should build your life around. For some people it is a career. But for others it will be family, religion, a hobby, etc. and those people need to find either an okay job or someone to team up with who has a career. And we need jobs that actually pay enough to live on, even the ones that aren't college career jobs. Telling people they're worthless is crushing. Telling everyone they're special is pointless if you don't help them discover what makes them special and how to do great things with it. Self-esteem is a superficial opinion; self-worth is backed by the intrinsic value of life and by the unique talents and skills of each individual. If you spend years telling people they're special and then suddenly go "Ha ha, I lied, life actually sucks and you're just a pawn," they will not only be unhappy but quite probably hate you.
4) And let's not forget the part where the elite among the Baby Boomers set the climate actually on fire and are now doing their damnedest to prevent anyone else from fixing it.
Yeah. No fucking wonder Generation Y is unhappy.