Insisting on what your (or your daughter's) feelings are is a type of gaslighting, it is invalidating.

"I won't bother caring" is a type of emotional blackmail, which is when someone inflicts emotional pain when you don't do what they want you to do.

What happens after she says "oh ok, I won't bother caring then"? An option might be to just leave it at that, let her "not care" and see if that stops her from denying people's feelings.

Another option might be to ask her about it, not in a confrontational manner but in a genuinely curious manner: "Why are you insisting that we are wrong about our own feelings?"