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First, she did tell them in her bird speak that she could and would transform into something, they just didn’t connect the dots.
Secondly, they didn’t just call her the legendary bird, the call her Devine and Holy bird because they can feel her holy/devine powers… those powers only come from one place, that’s why she legendary because they were waiting for something like her to be sent from heaven… so how wouldn’t they know instantly she’s an angel, if a creature with wings sent from heaven turns human, they should know, he should know if he was paying attention. She’s not allowed to say it, but she can keep him if he figures it out. The fact that he hasn’t yet makes him obtuse smh
Why couldn't she say that she could transform into a human I mean transforming into a human they won't assume already that you're an angel plus they already thought of you as a legendary bird or something so that would make a perfect excuse