It seems there are two schools of thought here. One is that the landing plane on final in this scenario has the right of way, and the other is that the plane that is on the surface having already landed and is back taxiing has the right of way. If you believe the plane on the surface has the right of way, you believe he doesn’t have to give way to the plane on final because the plane on the runway isn’t done landing yet, and won’t be done landing until he is at the exit where he can access his hanger. Therefore, he does not have to give way to the plane on final.
When you land at a controlled airport, you don't switch comms to ground control until you've exited the runway. The tower controls landing traffic, and until you leave the runway you are still under tower control and you are still considered part of the landing traffic.
This at first glance seems reasonable, but I have to go back to Oshkosh 2019. After I landed, the tower told me to exit the runway onto the grass to make way for the plane on final. The plane on final didn't declare an emergency, and I hadn't reached a taxiway exit either. It was apparent to me that now that I was on the ground and had slowed down somewhat, that I needed to give way to the plane on final, even though he hadn't declared an emergency or wasn't under any duress. Based on that experience, it would seem that the plane on final did have the right of way over me, and I was being instructed to make way for him. I mean if I was still the landing traffic, I shouldn't have had to make way for the guy behind me, he should have had to go around because I wasn't done "landing" yet.
I just think that the process played out exactly as the FAR's intended them to. The OP pulled off the runway, giving the plane on final the right of way. Again, I think the CFI handled it very poorly, but the OP did as the regs required. After all, the OP was operating on the surface, and since he was operating on the surface, he was required to give the right of way to the CFI on final. The OP wasn't forced of the runway, like I described in post 268, or even like I described my landing at OSH. He gave way to the CFI by pulling off the runway at a taxiway exit. It did not matter that It didn't go where he eventually wanted to end up.
In my landing at OSH in 2019, I wanted to slow down at a more gradual rate. Instead, I had to break harder and pull off onto the grass more quickly than I really wanted to. It was no big deal. We shouldn't be making that big of a deal on this thread either.