To me that seems like a purely post-hoc argument with no evidence to justify it.
For instance, imagine that the data were showing the opposite effect, that is, adults having a significantly greater increase in depression and anxiety than teenagers.
If that were the case, one could just as easily argue that it fits with the "our societies are so advanced that we can listen to mental illnesses" hypothesis quite well, because adults have the autonomy, resources, and maturity to get the attention they need to tackle their issues and symptoms. Teenagers don't, on the other hand, as they depend on their teachers and guardians and older adults often dismiss kids' symptoms as “not real illness” and just angst and moodiness.
I can only speak to my own experience but I suspect there is some generational component to the increased awareness of mental health issues.
I was in high school during late 90's and early 00's. I was not diagnosed with anything until 2009 (around the articles timeline) looking back in hindsight I struggled with issues for years, lack of energy (some days just dragging myself out of bed was chore), lack of motivation to do anything, I avoided socializing with people I had no energy to stay in touch with friends I would make excuses to avoid hanging out with people all of the time because I never felt up to it.
If I spoke up to family members etc I was told what I was going through was normal, everyone feels tired, in essence to suck it up and stop being a wimp. It got to the point I just assumed everyone felt the way I did all of the time.
It wasn't until by chance I saw a different and younger doctor one day for an unrelated health issue I mentioned (again) how tired I felt all the time lack of energy I had it was explained to me that what I was experiencing very much not normal. That was the first time anyone took what I was saying seriously. My life drastically improved afterwards. I was 24 at the time.
When I was a teenager no one talked about mental health it just wasn't done. So I would not be surprised if some component of the statistics is an increased willingness among medical personnel to notice and diagnose the issues.
That being the case, the point remains that a dismissive adult is much more likely to get in the way of a teenager from getting a diagnosis than that of another adult. Furthermore, the fact that doctors are more likely to take men seriously than they do women would explain why the increase in diagnoses is so much higher in male adults than in female adults, even though the base rate of women suffering from mental health issues is actually the same as that of men.
Obviously, the part in italics is fiction. It is referring to the alternate world I mentioned in my comment above where the effect was the the opposite of what we're seeing (with the added extra of adult men appearing to be seeing a greater increase than adult women) and how it's so easy to come up with post-hoc explanations using what seem like reasonable and factual premises.
For instance, imagine that the data were showing the opposite effect, that is, adults having a significantly greater increase in depression and anxiety than teenagers.
If that were the case, one could just as easily argue that it fits with the "our societies are so advanced that we can listen to mental illnesses" hypothesis quite well, because adults have the autonomy, resources, and maturity to get the attention they need to tackle their issues and symptoms. Teenagers don't, on the other hand, as they depend on their teachers and guardians and older adults often dismiss kids' symptoms as “not real illness” and just angst and moodiness.