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.
My libraries are mostly in Haskell, so depending on them is a matter of adding a line to a standardized build file. I have not yet received mail from a user asking me to change a license because they wanted to actually include code in their works -- it's almost always a misunderstanding of copyright.
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.