I know it's not my brother's fault that he has BPD, but is he responsible for his actions?
Yes. If you lost your job tomorrow (not your fault) you'd be responsible to conserve resources, perhaps file for unemployment and look for a new job. If I was injured in an accident (not my fault) I would be responsible for going to Dr's physical therapy appointments, paying medical bills, and following Dr.'s instructions for healing. You didn't ask to have a sibling with BPD, but you're responsible for managing this situation. pwBPD are less able to regulate emotions. It's not their fault. They didn't ask for it, but they are responsible for the impact of their behaviors. It does NOT mean we can mistreat them.
The mistake I made was to spend too much time expressing my hurt with the expectation they would change. (Not that they can't change, because some pwBPD do choose healing and recovery.) I came to understand that trying to control someone else's behavior is an expression of poor boundaries on my part. I was stepping outside of my yard trying to fix/rescue/change someone else.
You need space to be able to find your footing and rebuild. Giving yourself space to heal is not just loving for you. In many ways, it's the most loving thing you can do for him. It is not punishing him, but it is a natural consequence of his mistreatment, which opens up an opportunity for him to learn a new way of relating. He may not choose a new way, but you're giving him the opportunity.
I go back and forth between being angry with him and feeling sorry for him. I want to treat him with dignity but I also can't help but feel so frustrated with him and all the chaos his disorder causes to our family.
Pity means feeling sorry for someone while unconsciously assuming our own superiority. Compassion means feeling empathy for another's experience while maintaining equal dignity and respect among persons. Compassion brings insight, patience, clarity, tension and resilience that will often change
you from the inside out. Compassion means believing your brother is hurting and faces greater challenges than some (empathy), AND that he is capable and responsible (dignity). Compassion will keep us soft but will also keep us in our yard, prevent us from 'fixing,' and keep us humble. You're holding all of these seemingly conflicting emotions in your heart at the same time and that will stretch you.

Also want to validate that it's 100% ok to want space and feel frustration right now. This is a season. Process. Breathe. Take all the time you need and be where you are. Feel the intensity now knowing that it won't always feel this intense.