Disagreements are good. Disagreements are healthy. Disagreements don't need to get fixed.
I have noticed that there are some folks that need to 'fix' disagreements amongst their friends and colleagues. I think those that do this fall under two categories. First, their are people that take a disagreements personally. They react to any disagreement as if it means the other party does not like them. Therefore, they project that feeling of rejection upon any two people they see in disagreement. They then to interfere in the dialog between the folks that are disagreeing and try to smooth things over. The second type, sees any disagreement as disunity that must be repaired because the universe should be one big happy place.
The react-project combination is what magicians work to dissolve through detachment. This isn't avoidance detachment. This is being able to step back and see a situation for what it is, rather than what our own programming tells us it is. Often, our inner programming is as dumb as a computer's. Computers know one thing, on and off. That is it. Millions of interactions, calculations and outputs make that very simple action appear complex. It isn't.
We react to different stimuli the same way. Try this exercise. Go outside and stare at a cloud. When clouds occur every day we have two choices. We ignore them as part of the environmental background or we notice them (off or on). When we notice them, a chain reaction of memories occur. Nice and fluffy clouds may remind you of a string of warm pleasant afternoons as a teen. Storm clouds may cause a little pang of fear because they are linked to a weather patterns that destroyed your barn as a child and left you feeling vulnerable. These reactions are the 'on' part of things.
Detachment allows us to look at the storm cloud, realize that rain and wind may be coming and go about our day knowing that the average storm does not destroy the average five story apartment building in which one is currently living. We can then sit by a window and watch the clouds' oncoming attack with the same feeling of peace and serenity invoked by the fluffy clouds.
Those that feel (likely unconsciously) that an argument is a sign of disunity are in the same trap. The universe is a cohesive whole. That doesn't mean conflict is not a natural part of that whole. There is a conflict between the force of a waterfall and the rocks below. Such a conflict results in beauty. There is nothing that needs to be fixed.
Those that seek to interfere in the conflict are reacting to programming. On/Off. Input/Output. The illusionary complexity of human interactions allows us to convince ourselves we are willfully applying our minds. In truth, it is detachment that does so. That detachment allows us to be fully actualized humans rather than computer-like reactionaries. That detachment allows us to be magicians with purpose, rather than a computer with a few more input/output devises.