An intractable argument is one, to me, that has no agreed upon answer. Said another way, there is no right or wrong answer, more an opinion. And I am confident those who hold opinions are sincere in their beliefs and thoughts.
Here's examples both from today and our past.
Is a person ahead of their time, or just using poor judgment for today's time?
Should women be involved in infantry combat in defense of our Country?
Do you think long term or short term? And which is a better way to go for the situation? The obvious example, to me, is one of strategy in prosecuting a war, and is the intent to win the war, or the peace which will follow?
Should we aggressively attack and accept the inevitable casualties, or drag out the attack over a longer period of time, and hopefully reduce casualties?
Who suffered worse with attacking casualties in WWII? Was it the 8th Air Force, the Navy, or the Marines?
Is it best to bite the bullet now, or just muddle through as best we can?
Now getting into personal lives and finances I decline to get into these days. But that subject is full of intractable arguments, too.
And last, should we graduate a class early, like I know West Point did for WWI, and the Naval Academy did for WWII, or just keep up the regular schedule?
Good luck if and when you enter into this arena!