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Primitive man sees nothing impossible in the story that his tribe is descended from a beast or a bird: the lady in the fairy tale who married a bear or a snake was doing nothing particularly improbable. As knowledge advanced, these animal husbands became enchanted men who regained their true shape at last, but this is a later modificaion to suit later ideas.
About the part in bold, is it about the character that undoes the spell and becomes a human being at the end of the story?
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Yes, it implies that the bear or frog has been human all along, but were simply in the form of another animal.

I guess in primitive fairy tales, "and the beautiful lady married the bear and they lived happily ever" after was okay. Now, we'd say "And with that, the spell was broken, and the bear once again became the handsome prince, and the beautiful lady and the handsome prince lived happily ever after."
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Great! Thanks, GG!