Hi there, I'm so sorry for your pain.
He has told you the problem, but for a non bpd it might be hard to see, but I think you do see it, it just doesn't make sence to you.
he says he just feels like he isn't worthy of me.
This is one of the main symptoms of bpd. That is why we test, run off, isolate ourselves, hurt ourselves, etc. Or some of us do. I do I know.
How does one suggest to a borderline, that they are worthy?
That is the hardest question for me to answer, Nothing anyone says can convince me I am worthy. All my childhood and some of my adulthood, I not only was told over and over what apiece of $#%^ I was, but was abused because of others fears, acquisations(sp) and had me totally convinced I was a mistake on the earth, and didn't deserve to breathe/ . With kind of history only therapy, and years of love and dedication by my spouse has helped me in to the recovery stage. I no longer punish myself, when there is no one to do it for me.
I like or hate, I cannot describe love. The only way I can is the feeling I have for my pets. They can't hurt me, lie to me, punish me, run me off, judge me. But when they pass on, I feel like I am dying inside.
BPD's live in shades of black and white and the grey is impossible to muster, as we were not allowed this part of learning and receiving, or just couldn't handle doing it.
Your boyfriend IS SURE, that he is unworthy. He really believes this.
If you can try very hard to imagine living your whole life feeling this way , without constructive reality to re-enforce that you are a good person, you might have the key.
All my best to you both,