Presumably, User wants to include your library in their open-source BSD release. If that is the case, what they're asking is correct since a work extending / modifying a GPL licensed code needs to be released as GPL as well. That is the main difference between GPL and non-copyleft licenses.

They could distribute their code without your library, as you say, but that would require more hassle from the end-user, especially if there's some configuration / integration process that is required to make both work together.