The book mentions broad tags as needing to be narrowed, and that characters can only have one, but does this mean per character or per character card? Most of the power tags in the A section are rather broad, and if I understand correctly you need to answer the first power tag question.
[Y]our character can have only one broad tag.
[... there is a] single broad tag allocation available for the character.
-- City of Mist Player's Guide, p. 77
"Broad tag" refers specifically to a way to classify the power tags across all your mythos and logos cards. Other elements like weakness tags or mystery/identity definitions aren't subject to the specific/broad/too broad evaluation.
However, there are two options (on that same page) to make a broad tag less broad.
The first is to qualify it, adding additional description about the circumstances or limits of the tag. Usually this is more fitting for Logos traits, to turn, for example, cunning into cunning negotiator.
The second is to gate it, saying that while the tag represents a general capability, in order to count it as a power tag, you need to first create a more specific story tag using Change the Game. Usually this is more fitting for Mythos traits; Adaptation, the one that most often would start out with a broad tag to answer its A question, also gets an advance to go Dynamite! on a Change the Game roll.