What should I say at this point in an argument?

Multiple times with a friend, there comes a point in our argument process where she has made a point that is logical and not wrong. While I am still unconvinced – I am unable to argue farther. I decide her point is no farther from the truth than mine, so until more information or perspective presents itself, I can’t go further in the argument.

At this point, I say “Fair.” She finds this upsetting. I don’t know how else to express this point of view, and she doesn’t know why she finds it upsetting, aside from saying she finds it an inappropriate use of the term.

Thoughts? Help? Ideas? Insight?