People react to stress differently, what breaks one person might not break another person. And some people are just inherently prone to mental illness regardless of what happens to them due to genetic factors. Kaladin had issues with depression even when he was young though they were of course made worse by what happened to him.
As for not realizing it, if somebody has had problems since they were very young they might not realize it's out of the ordinary because it's just normal for them. Or they could deny it (consciously or unconsciously) because of stigma against mental illness.