Ah, but tragedy does not equal horror, gore or violence. Originally a comedy, for instance (like the Greek comedies) was not a funny story, simply a story which ended happily, while a tragedy ended sadly, as in the lovers did not get each other in the end (or like Romeo and Juliet they died).
I think it's because a tragedy, a story with an "unhappy" ending, speaks to something deeper in us. It rings more true than a story where they live happily ever after. We know that's simply not the case, most of the time. Life is not a series of happy endings.
And the stories, at least the Greek ones, were often about something else than what they appeared to be on the surface - comments on society, etc.
The folk tales, as in the Brother Grimm tales, are also often tales about archetypes which help us deal with difficulties in our own lives. Bruno Bettelheim has written some very good books on this. He has these theories which I can't shortly explain here (or even remember very well...) about how a child can deal with it's negative emotions towards it's mother through stories with wicked step-mothers, like Snow White etc. They were not just stories for entertainment. They were old tales that had been passed on orally for generations, containing old, deep truths. They were projections of desires and wishes and reflections of reality. They were not meant for children, not before The Brothers Grimm wrote them down, anyway. Their stories were indeed aimed at children.
Oh I am rambling again... I can never explain things properly.