I saw this sentence in Duolingo. Is this supposed to be dative? If so, why?
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The verb glauben can take both an accusative and dative object. The something you believe is accusative, the person who you believe is dative.
The dative form of mein is meinem. Again, Wiktionary is quite a good help.
Thus, it's correct to say:
This is a possessive pronoun, dative, "male" grammar-gender.