Why do some people find it hard to accept losing an argument or even settle with 'agree to disagree'? They have to have the last word. Low self-esteem? Self-importance? Arrogance?
And how do you deal with such individuals?
It's not limited to differences in political views by the way.
Thanks for your input and wisdom in advance.

It’s unfortunate to know there are some individuals who refuse to accept losing an argument. There are actually various amounts of reasons why this is handled this way. Making assumptions for the reason why can seem overwhelming, but could be eye opening. It really depends on your own level of patience and the other persons level of arrogance.

If the other is willing to listen you have a good shot at getting through to them. This could be through logic and fact checking. Usually using reliable sources can wedge doubt in the other persons thought pattern. For me, it’s not about getting the other person to agree with me but to see a different perspective.

I’ve come across people with different reactions, and the best advise I can give is, is it with trying to convince them to change the other person’s thought pattern or get them to see there’s more than once side to things?

Do what makes you happy, because at the end of the day you want to be content.

EVERYONE'S root philosophy is opportunistic or they would be dead.

The argument is only who is willing to expose their morality most adjacent to that.

Once you discover that the other has a different level of public morality, there is NOTHING you can do to change their mind rhetorically. Physical influence must be introduced-- a piece of candy, money, etc.

Unless violence is used, an argument is ideological.

To lose an argument is to acknowledge that either your competence or morality is inferior.

Ultimately at the root of every question is the split philosophy: Opportunistic vs Altruistic.

In public, one must be seen as Altruistic. If the opportunistic morality is allowed to be seen, you can't be trusted.

Trust is the only thing of value.

If you lose an argument, you potentially lose trust.

To lose trust is evolutionarily a death sentence.

Money has replaced trust as currency. The dynamic has changed.

Someone who refuses to accept losing an argument, or conceding stalemate, isn't interested in having a relationship. They are interested in exercising power over others. I deal with such individuals by not having a relationship with them.

The objective in any discussion should be to discover the most unassailable principles that apply to the situation. These will point to the resolution. With that approach every question is resolvable. There will still be people who will not accept the resolution and that is because of a stubborn refusal to consider any argument that goes against what the person wants to believe.

I personally have a problem with those who try to use the "cop out" of stating that "we'll have to agree to disagree". In 100 % of the cases where I've heard someone use that lame excuse, each had no idea or any significant knowledge about the topic in which they chose to argue (not debate). In each case, without exception, the person decided to claim something wrong about a topic or in several instances butt in to inform others that they were wrong, without ever providing a legitimate reason.
Such people are simply rude, uninformed in the area in which they are arguing, and too mentally weak to actually do the research needed to gain any insight into the topic.

"I've always felt that a person's intelligence is directly reflected by the number of conflicting points of view he can entertain simultaneously on the same topic." Abigail Adams. It's rare that there is only one point of view that is valid. It's rarer still that one can find people like Abigail spoke of.
An argument ensues whenever one party cannot accept the other's point of view and tries to prove themselves right and the other wrong. As Edgework pointed out, the argument usually stops when you allow the other to be right, however, I have found out that for some argumentative types that's not enough. Best to walk away on the high road with a smile.

Because they consider themselves to be correct

You answered your own question as to the why. As to the how, usually not much you can do about people like that. Just abort if possible until they wake up. I know that's not a helpful opinion and discouraging, but that's the best I have for the moment.

I hate landing on "agree to disagree"... that means you just wasted each other's time.
If you truly disagree, and you're actually talking about the same thing... which isn't a given; then that means at least one of you is wrong.
If the topic is meaningful at all (and if it isn't, why are you arguing?), then it might be useful to figure out which it is.

See "Cathexis."

Sometimes we have reason to think we're correct. Having said that, sometimes just being right doesn't satisfy, so what else is at work? When you see someone trying to cut a tunnel through granite and you know there's a path around the hill, the inclination is to offer another way. Not everyone wants to take that way. And not everyone can accept that. And of course, they may be digging the tunnel for entirely different reasons than getting to the other side. It behooves us to remember that our assumptions may be in error.

Often, there is a needfulness on both sides of an argument. On the other hand, maybe a child is watching. Then what? Is the lesson about the issue at hand, or is it about comportment? It's almost never a life or death issue. On the other hand, what if it is a life and death issue? Knowing the difference makes a difference.

Generally, the person who HAS TO WIN, is committed to something, but what that something is can range from Truth to Self-aggrandizement to Narcissism to Deceit to Neurosis to Guilt---and a million other things. In the end, you can only come close to knowing yourself.

And this addendum: The most compelling reason for needing to win is tied to Survival or perceived Survival, usually as a matter of personal identity. We get pretty fussy when we feel that a piece of ourselves is being chipped away. I know I do.

Most people who we revere as wise or competent often come across as arrogant. Philosophers, politicians, scientists, pretty much the top section of any hierarchical structure. Especially when you get into matters of truth, no one likes lukewarm people who can never stand for anything and sway to and from depending on the weather and the state of their digestion. I think there’s an important difference between a wise confidence and arrogance. The difference is humility. Whenever I come across someone who acts as if they got things figured out, I count it as a mark of a fool. A wise man knows how little we really know...I can see how even that may seem arrogant lol

Once it’s clear they aren’t interested in a free exchange of ideas, I’ll say, “So your position is X, Y, and Z? Do I have that right?” When they agree I say, “Ok, Got it.”

Whoever next fills the following silence, loses, whether they realize it or not. If they push their point further, I nod and say, “Really. I got it.” If they get angry and want to argue, don’t. Eventually they’ll go away with only the sound of their BS ringing in their ears.

I ignore after the third "yeah but....".

Saves on my cannabis costs.

Everyone suffers from feelings of insecurity at some time and/or in certain situations and those that appear arrogant or full of self importance are usually behaving that way because they are insecure. If you really are confident in yourself you don’t care what people think or what they think about you so you don’t need to be arrogant or to have the last word.
It’s difficult to take on board but most people’s behaviour is more about themselves than about the people they are interacting with.
This also applies to debates or arguments although the actual subject of what arguments/debates are and how they work in practice is a subject in itself and can cover volumes.

My ex was like that, always had to have the last word no matter what. Over time, and only after I divorced her, did I learn to have fun with it. She called me long distance once, and my mom was visiting at the time. The ex had a fit about something for about an hour, and when she was ready to hang up I said the right thing to get her riled up and carrying on. I kept her on the phone for over 4 hours. My mom was confused, but when I hung up I explained the call was on her dime, and this was before cell phone with the cheap long distance calls. That call cost her quite a bit. Humor was the best way I found in dealing with her. Always find something about the situation that could make me laugh.