I think I don't start off agreeing with your premise about "owning your stuff" because I think there are more possibilities than your transference or his transference causing the problem. Sometimes people just experience the same interaction differently-- perhaps most of the time-- and while I do think the past is powerful in interpreting what others say and do, sometimes there just might not be something to own up to. There are times when the most honest thing to say is that you see it differently, and refuse to take responsibility in the way that other people want you to. I've been on the receiving end of someone wanting me to take responsibility for part or all of something that isn't mine, and I in general won't do it.

Perhaps this is just another way of saying its transference, but when I bump into an interpersonal problem that I can't make progress on, I try to reframe it as something more symbolic. There was a slow change over some years a while back, where it was very important to me that people own up to doing something that upset me. I was prone to pinning them against the wall and not letting up until they'd satisfied me that I'd be heard and they planned to change their ways (not an actual pinning, btw). This was an important transformation for me because I hadn't ever tried to resolve things with my loved ones in a meaningful way, I'd either chew them out or leave them without explanation or much chance for them to say anything. People who were afraid of losing me or afraid of confrontation would usually just give me what I wanted, but when I tried this in therapy, it didn't work so well. My T, who is one of the least defensive people I've ever met, would offer an alternative perspective, apologize for any misstep or mistake, and state his intention if it was different than my interpretation. And he did this all in a nonjudgmental way, but what it left me with was an uncomfortable sense of non-resolution because it was different combinations of me owning up to my part in something (usually misinterpretation or overinterpretation), him owning up to something (mistakes or hindsight realizations), remembering things differently, and seeing things differently.

I am not sure if this is where you are, but I think that many difficulties/disagreements/conflicts with people cannot have some neat resolution that is always satisfying. Understanding that others don't always see it the way I do and being comfortable with that put me in a new place in my relationships with people. Being able to move forward in therapy while regularly not seeing eye-to-eye with my therapist has been helpful to me in general. It is useful in understanding myself, sometimes seeing a very long chain of things that are tied to my past, or about who I've become as an adult, or both. I do see things in general differently than many people, and that is one of the things I actually most value about myself now.

So I don't really see resolution, or owning up, or whatever as the end of conflict or disagreements, as the end point. For me the endpoint is understanding, including understanding that the other person feels and sees and experiences the same interaction I did in different ways. It's an opportunity to learn more about myself and the world. Therapy was the easiest place to practice this, because my T has the least stake in the outcome-- he was comfortable and still is, with us disagreeing. I think it takes a person with a strong core to not cave into someone who is insisting, very strongly, that it must be X and not Y. And I realize that developing a better ability to agree to disagree and talking for purposes of understanding and not changing someone's mind was great preparation for raising a teenager. Especially my own Alex P. Keaton-- for the youngsters here, a character from a popular TV sitcom of the 80's, a conservative kid in a family headed by post-hippie, liberal parents.