I agree, but it feels like I owe them, rather than the other way around.
Perhaps this indicates that you're thinking of the thing you currently believe as "your" position, and of persuading the other person as "winning" an argument. The present discussion aside, you might want to try to change that.
Would it be supercilious to thank someone for updating? I know I would feel uncomfortable doing it, but I often feel the urge to do so anyway.
There seems to be something vicious about thanking them. My own estimation of my own belief has not changed in these situations. I feel fairly satisfied that the other has considered my view and has shakily come to agree with it. I worry it would be a little like saying 'screw your opinion, now you see I'm right.'
However:
It is both rational and polite to thank them. The gentlemen's agreement of rationality allows for one person to be wrong and not lose face at all. When someone concedes something to me (a point) I typically feel the need to thank them.
What do you think?