It is not really all that rational. "A few bad things happened, so obviously the world is crap" is an emotional response of the sort normally associated with adolescents. I have plenty of contrary anecdotes of my own, but they would also not prove a universal truth about the world.
True enough, but one must tread carefully. A history of mental illness that demonstrates that you were a threat to yourself or to others is going to impact your residency in the US if you are an alien. A history of alcoholism (and depression may lead to alcohol abuse) with evidence of past harmful behaviour is going to work against you.
I am fortunate to be healthy, but if I weren't, would I tell anyone? Probably not. I like the US and want to stay here.
I can't name a single person in my life who has sought help and not been punished for it. I have, fortunately, learned from their mistakes, and will never seek help myself.
I can't see how it isn't rational. I have ample evidence seeking help is bad. I have none whatsoever that it's good. The rational choice is objectively obvious.
There's even a doctor in this very thread defending that punishment as "first-rate care"[1]. What other proof should I have before deciding mental health care has nothing to do with caring, and everything to do with punishing and isolating people who are inconvenient?
No; cynicism is intellectual and moral laziness. It allows you to distill a complex world to a simplified negative caricature that justifies not making an effort yourself (or makes your efforts seem more extraordinary than warranted).
My personal counter anecdote: 2 weeks ago, I lost my camera (with a nice new lens on it) in the subway. Worth more than $700. Everyone I told said almost the same thing: "you'll never see it again, someone would have to be stupid to give it back; I would, but I'm stupid."
Well, 2 days later I picked it up at the lost&found.