Why ‘agree to disagree’ is such a horrible thing to say.
First of all it is contradictory. Are we agreeing or disagreeing?
If all it means is, “We agree that we disagree,” then it is a pretty silly thing to say. We both probably knew that earlier in the conversation.
If it means, “Let’s agree that we will continue to disagree,” then it is pretty stupid. The whole point of a disagreement is that each person think they are right and would be very happy if the other person came to see things in the ‘right’ way! No one in their right mind would really say, “Let’s agree to continue to disagree!”
But if it means, “I don’t want to talk about this so you have to shut up,” then it is contradictory, because it isn’t really based on an ‘agreement’. If both of you want to shut up, well, nothing’s keeping you talking! It is only when one of you wants to stop talking (perhaps because they are losing) that the infamous ‘agree to disagree’ raises its ugly head.
Which brings us to the second problem with the phrase: it is a form of blackmail. If the second person doesn’t ‘agree to disagree’… i.e. if they wish to continue to present their argument, well, then, under the modern rules of the game they are being ‘disagreeable’ and ‘argumentative’ and ‘unloving’ and all sorts of nasty things. So the second person is being forced to shut up by the first person (who, often, accompanies their ‘agree to disagree’ comment with a parting shot, and wishes for it to be the last word on the subject).
The third issue that raises its head goes to the foundation of the issue: should we be discussing this at all. There are two choices:
… Because in important areas of life our goals should be to seek the truth, to let iron sharpen iron, to always be ready to give a defense… If the subject we are discussing is actually an important area of truth, then agree to disagree is precisely the wrong thing to do!
Now, I believe there are some ways to sign off a conversation at least for a little while.
In the lighter ones, "Hey, I have to go now, it's been nice talking to you."
In the heavier ones, "Wow, you've given me a lot to think about. My brain is about to pop. I'll get back to you later on this subject."
One time when I think it is a real mistake to bow out of a conversation is when the person is being annoyingly obtuse… perhaps even full Cathy Newman. In those cases I believe it is important to realize that in many cases (as Cathy found out) a lot of other people will be watching, and if you handle the situation calmly and well, you will convince them... even if you leave Cathy in the dust.
Isn’t it mostly a conversational gambit used to end an unproductive conversation? If someone doesn’t want to speak and you try to compel them to, it’s aggression - even if you have justification withinin your own value system for trying to force the issue.
It’s kind of like a door-to-door canvasser who physically keeps you from shutting your door, to compel you to listen, because they think they have something important to say.
Your theory creates a bubble that this is the correct idea and no other idea need to be discussed. A majority of people apply the thinking pattern there prespective is correct. Agree to disagree is you engaging disturbance into your bubble while keeping civil and not canceling conversations. People will always hang themselves with bad ideas, so open engagement where everybody can observe is the best we can hope for.