Like many things it's multifactorial. Not so long ago, mental health issues were mostly ignored or people were simply expected to HTFU. This recognition that psychological illness is as real as organic illness is a good thing.
It has been speculated, that in the absence of actual threat – in general, most of us in the developed world live prosperous, risk-free lives, we're not going to get eaten by a tiger or have to go to war – we turn mentally inwards. We're primed. In some ways there's an analogy with the immune system, where – in the absence of actual challenge – it turns to autoimmune disease and allergy.
We also live in a world driven by falsity. Happiness is a shiny car or whatever else they can sell to us. Except it isn't really and I think that subconsciously we all know it. We're chasing the unachievable – whatever it is, we won't be any happier when we get it. We're primed in so many ways to be disappointed. We build a scaffold of our expectations. I never considered it a privilege at the time, but growing up with parents with zero expectations of their son was quite nice. Having traversed to the middle-class world I know parents who are fretting about where they fourteen-year-olds will go to university. Some of that has to transfer. University, jobs, houses. Then media. The latest clothes, how you should look, when I was younger there wasn't the constant bombardment of advertisements. It applies to everyone of course, but I think younger people feel it the most, of course (and that's borne out in the stats). They grow up in a world of constant expectation pressure from all directions. There are innumerable examples. We did exams once a year. A horrendous burst of stress, for sure, but for 90% of the year you could fuck about. Now we dose out stress throughout the year, a steady toxin.
I think another reflection of that pressure is an unwillingness for parents to potentially damage their child with a 'no.' My childhood was a symphony of noes. I rarely had to finish my request before it was no-bombed into oblivion. Nowadays everything seems to be a negotiation ('now then Poppy, stop stabbing mommy, you don't want bloodstains on your dress do you?'). It's probably a good job I don't have kids, I'd probably be awful (and actual parents can tell me to 'fuck off' at this point). Every Friday, I have to wait while no fewer than four adults try to herd a class of kids out of the swimming pool. It's endless negotiation and cajoling. No 'stand there and be quiet.' This observation may, of course, define me as officially old. But in a world without noes, that feeling of expectation can only grow.
There's also a strong correlate with social media. Pressure is no longer a local phenomenon and every kid seems to go direct from dummy to phone these days. I doubt that bodes well.