The Fallacy of the middle ground is the belief that two extremes are best resolved by compromise. The power of this argument draws from the observation that it is often true.
My neighbour claims that the fence is ten feet into his yard, and I claim that the fence is ten feet into my yard. It's reasonable to just leave it where it is, because it's exactly even between both our claims.
After the accident, both drivers claim it was the other's fault. A good settlement would place them both as half to blame.