>The existence of a male mental health

Maybe you can you disambiguate your phrasing here. Which do you mean?

1.There is a MALE mental health problem -- some mental health problem wholly or partially unique to men

2. There is a mental health problem observed among men

If #1, where is the evidence? A men-only survey can't show it. If you surveyed left-handed people and 30% had anxiety, that doens't mean there is a left-handed anxiety problem.

If #2, we agree on what the research shows, but it brings your original point into question: "Isn't recognizing there is a problem the first step on fixing the problem?" Which problem are we recognizing? Labeling a general problem a male one assumes a diagnosis, which points the search for causes and fixes at men when nothing in this report shows that's where they are, and other available information shows worsening mental health in women as well.