There is truth in the original saying. Adversity creates the conditions and provides the motivation that spur people to develop strength they would not have needed otherwise. However, adversity is a very blunt instrument, and it is also a matter of degree. People don't always respond positively to adversity. And if the hardship is too great, it doesn't lead to opportunities for growth, just trauma.
That's one of the reasons we need safety nets, to dull the hardship to the point where we can grow through it and not be crushed under it.
That statement comes with the implication that strength is something intrinsic and static. That's not true - you get strong when you train, but you have to train gently and gradually enough to not get injured. You train yourself to be physically fit, but if you push too hard you will sprain tendons and break bones. You can also train yourself to be gentle, and if you push it too hard, you'll be taken advantage of. You can train yourself to be assertive, but if you push too hard you'll end up being aggressive and alienating people. That's part of growth.
Saying that adversity filters out weakness - no, adversity pushes people too hard before they're ready to handle it, then they fail. Sometimes they try again, sometimes the damage is too great and they give up. That's not a moral failing though. It just means they were pushed too hard.
i.e. they were too weak. strength/weakness in this sense has little to do with morality. someone who can't rise to the occasion or hasn't grown enough isn't a bad person or anything, just unprepared or ill suited.
e.g. a natural selection even doesn't care if an organism was still growing and learning. They either survive (strong) or die (weak). And that's the same definition of strong being used here.
It's called hormesis. Yes, there is a range beyond which further stress causes permanent and serious damage, but within the hormetic range "adversity" is basically the proximate cause of growth.
Stress impact also varies per individual biological differences.
According to Sapolsky's lecture on depression [1], a stressful childhood experience is 30x more likely to cause depression in individuals with a particular serotonin-related gene variant.
No. [1] The context of the whole conversation is traumatic relationships. If anything you are talking about eustress - and traumatic relationships are not beneficial and do not "make you stronger" [2].
That's one of the reasons we need safety nets, to dull the hardship to the point where we can grow through it and not be crushed under it.