Rather than telling her to break up with you, why don't you engage her in a conversation asking her what she means by this?
In other words, something like, "You say that a lot, but I don't know what you mean by it and it's troubling me. Are you sayiing you're tired of the relationship, and do you want to talk about that, or are you saying you're not sure about feeling this familiar?" or something to that effect.
The way you're responding right now shuts down communication rather than enabling it.