Which implies that at least one of you is dishonest or irrational or too lazy to continue the debate. ;)

See: Are Disagreements Honest? by Tyler Cowen & Robin Hanson, 2002

Interesting paper. I guess the biggest problem here lies in the fact that there can only be so much truth seeking. So, with more time and effort, we could come to a conclusion that suits both. But... I don't have that time, to be honest. ;)