Why does he say "my child" even though Cinderella is not his child?
This is a term of endearment. He is acting as a kind and caring person, almost like a "fatherly role." Since he is an elder, he sees Cinderella as a young child. He is trying to show Cinderella that he cares and that she can trust him. He is acting as an elder in an affectionate manner.
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