I couldn't challenge him on it, because then it feels like I am questioning his competence. I just kept quiet.
If you are confused and really don't agree, it's completely reasonable to keep asking questions. I always have several questions for my doctor...and I've stuck with her because she is willing to answer, if she can, or have a conversation about stuff.
Does he feel like he needs to nail a diagnosis for treatment and/or insurance purposes? Like this might be more descriptive of the approach he wants to use in therapy? Does he not feel like sticking with just "PTSD" from the DSM will cover it? What is his driving force for giving you the diagnosis of BPD, even if he doesn't agree with the DSM? There must be something.
You deserve to have confidence in your therapist. It sounds like he wants to give you a diagnosis he doesn't entirely believe himself. So, I'd keep asking questions. It's your treatment. Personally, a DBT or other BPD approach would have been a far cry from the trauma therapy I am doing, and likely not as deeply relevant and helpful. Is he going to work with your traumas? And how? You are the customer/recipient of this uncertain diagnosis and what it might mean for your treatment.
You don't have to question his competence, but you can question his own uncertainty (as well as your own), and ask questions about why the diagnosis matters (especially since he doesn't agree with the DSM) and how this will relate to your treatment. It's helped me so much to be more active in my healthcare and therapy this way. You're not telling him what to do or how. You can just ask more questions and get more information so you are more empowered in your own therapy and healing choices. If he's determined to diagnose BPD but can't well explain how it fits for you, or explain a mode of therapy that you believe in, you have the option of finding another therapist who might have a very different interpretation of early trauma and diagnosis.
ETA a sidenote: I think this is where the Judith Herman work on trying to re-label BPD as CPTSD has not been very helpful. For one, we don't have a DSM diagnosis for CPTSD yet. Also, while many BPD patients might likely not be BPD but more some version of complex trauma (so deserve a more descriptive diagnosis and treatment), many others with BPD have no trauma history. So now sometimes people with obvious trauma histories can be diagnosed BPD because we've learned there might be a connection but we have no other diagnosis. So, a sort of back-fire effect while it all gets sorted out?
I think many therapists do see the separation here, that they probably can't be one-in-the-same, but it got muddied when the concept of CPTSD arrived. I've had a highly self-destructive history, but not the relational problems that are quite hallmark in BPD. In all my ins-and-outs of psych wards and therapists and hospitalizations for suicide attempts, I have not been diagnosed with a personality disorder. The skills work for the true BPD diagnosis would make little sense for me. Work on body-level regulation for the trauma has helped. I've moved beyond self-destruction but still have chronic pain, feelings of numbness, and avoidance of relationships. This relates well to my trauma, not so much my personality.