to hit on someone, to flirt
Depois que a nova vizinha chegou, ele vive arrastando as asas para ela.
After the new neighbor arrived, he keeps hitting on her.
The expression comes from the courtship of birds: a rooster woos the hen by dragging one wing along the ground as he circles her. From that display, arrastar as asas ("to drag one's wings") was transferred to people, describing someone openly courting or flirting with the object of their affection.
Sources: Só Português, Priberam.
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