Certainly that is an example of unstable emotional response. BPD and bipolar can share some similarities. BPD involves far more rapid cycling of emotions than bipolar and cannot be effectively treated with medication as bipolar can.
I was talking to my therapist today and telling her some is the things he does and she asked “has he been diagnosed with BPD? Because that’s what it sounds like he has.” I can deal with the emotions, what wears away at me is him constantly ending the relationship
