Oh, that does hurt, doesn't it? I think all kids do that at one time or another.
I think it's important for them to know that no matter what they say or do, our love never goes away. On the other hand, we also need to show that you don't get to say whatever you want all the time, as they get older.
When my little guy (5) says that I know he's feeling overwhelmed by his emotions. I don't spend a lot of time discussing and I keep it very cheerful, but I say something like, "I'm sorry that you're feeling that way right now, and I will always love you."
When my older son (9) said something hurtful not long ago I felt like he is old enough that he needs to exercise some moderation. I didn't get angry, but I did say something like, your feelings are important and it's good to notice when you are angry or upset. But your words are also important. It's ok to be angry with me, but it's not ok to hurt my feelings.
I think it's one of those things that depends on the child. But whatever seems right, don't let it hurt your feelings - I think it really means that she is feeling safest with your love because yours is the one she is testing.