To have a great disagreement: First, have great agreement.
Find that one point, one moment, one thing - that both can say with great certainty: "On this at least, we agree".
Anything else is a tragic shouting match.
Three ways I try and find this agreement:
Time frame - check that all are arguing over the same time period. What should happen over the next 3 months is different from what needs to happen over the next 3 days. Start here, it's almost always different in everyone's heads.
Walk up - If we can't agree on how to do it. Can we agree on what to do? If not, can we agree on why to do it?
Walk back - where last did we agree? Can we get back there and see where we lost each other?