Validation is difficult. It’s much easier to
try not to invalidate. https://www.bpdfamily.com/content/communication-skills-dont-be-invalidating
We frequently say here “Don’t validate the invalid.” Validating the irrational definitely falls into that category.
When you told her you love her, you invalidated her.
Crazy, yeah. I know.
You’ve got to keep in mind that people with BPD are not mentally organized in
the same way as those of us who are “nons.”
For them,
feelings equal facts and there is no way we can make a logical argument strong enough to persuade them otherwise.
So when you told her you love her and she doesn’t feel loved (most likely a feeling she’s had since childhood—and not your fault), you invalidated her.
What you could have said instead would have been some version of this: “That must be so difficult to feel unloved.”
Depending upon how she responded to that, you could take a step further. “I’d like to learn how to show you my love. Can you teach me how to do that?”
It may or may not work, depending upon how worked up emotionally she is. The closer she is to a calm state, the more potential for success.
However you can do it, it might be worth pursuing how she feels love. You might have heard of the different Love Languages: words of affirmation, quality time, receiving gifts, acts of service, physical touch.
I’ve had some issues with conflicting love languages in my relationship. For me, acts of service is how I express love and what makes me feel loved. For my husband, it’s words of affirmation and quality time.
I hear words of affirmation and I think, “Actions speak louder than words. Words are cheap. What does this person want from me? Yeah, right. You think you can manipulate me through compliments?” So obviously words of affirmation doesn’t have the desired effect of communicating his love, but now I understand his intention better, I realize he’s trying to show his love.
Likewise when I do something for him—“She’s always
doing something. Why can’t she just spend some time with me and (tell me how wonderful I am)

“ is what I’d imagine he’s thinking. Though as we’ve understood each other better, when I’ve helped him with projects, he has realized that it’s a way of telling him that I love him, and he’s been appreciative.
https://www.5lovelanguages.com/