If you think in terms of a hyperdimensional phase space defined by every human neuron (which I call "human cognitive space"), there's something marvelous about a disagreement.
It's like parallax, in astronomy. Most stars are so far away that we can't directly measure their distance. Some stars are close enough, though, that we can detect a tiny shift across the background sky as the Earth orbits around the sun. If we measure the exact position of a star in January and find it has slightly in July, we can triangulate and calculate how far away it is.
I visualize a disagreement as a rectangle defined by two corners. The further apart the upper left corner is from the bottom right of such a rectangle, the bigger the area. That's a good thing, in cognitive space. The area inside the rectangle is one might discover something new!