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.
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.