Consider arguments about how things are in the world or how things should be done — is there evidence of Bigfoot, is religion good or bad, is Obama a good or bad president, what we should do about conflict X in country Y, whatever. All too often, these involve people talking or shouting past each other, unable to agree about anything. The main reason for this is probably that they just start from such different positions that they can’t even understand what the other is saying or consider whether even some of it might be right; the opponent just sounds like an idiot that keeps saying obviously false things all the time. Another thing worth noting is that people tend to be emotionally invested in their basic, overall beliefs about the matter, and will not easily change those.
Here, I want to point to one thing that follows from this problem, one way of doing things that can improve the matter at least a little. If the conversation is to lead anywhere at all, you can’t try to do everything at once. In fact, since it would take so much energy on behalf of both parties, it may not be feasible to do “everything” at all — everything meaning correcting every wrong belief of the other person or, if we’re less arrogant, adjusting both of your views to the point where you can agree. Sometimes, all you can even hope for in the argument (unless you think a shouting match is somehow desirable; it’s not, though) is to make some little, local correction that brings you and the other more to the same page.
What does this mean in practice? Well, let’s say you hear someone say Obama has committed buggery in the Benghazi affair and should be impeached because of that, and the guy saying this is obviously buying everything his opponents are saying about him, whereas you think the opponents are just throwing out random nonsense accusations at Obama to turn people against him and/or because they’re paranoid for no good reason, and also the Benghazi affair is not a big scandal but just another example of something being blown hypocritically out of proportion. Well, it would be a huge debate to prove to that guy your general stance on Obama and Benghazi, and would probably never work anyway, but if you just explained that that’s not what “buggery” means and it’s not an impeachable offence anyway, you might at least decrease the other guy’s ignorance a little. It might be useful also to say that what exactly is going on with Benghazi is something that could be debated about (and you don’t agree), but you understand someone might disagree about that (at least based on what information is going around), and you don’t want to get in that debate — but this part is obvious and you should both be able to agree about that. If you only said it along with a lot of convoluted arguments about the rest of the issue, though, even this one obvious thing could be missed. (Disclaimer: I hardly know anything about the Benghazi affair, I’ve just noticed people talking about it.)
In an actual example, some time ago, I encountered someone on Facebook saying something in the lines of “feminism was never about equality and it’s dangerous because women already have more power.” Every bit of that seems wrong based on what I know, but to prove all that — really give someone who disagrees a reason to believe it — I’d not only have to give lengthy explanations but even study the subject better to be sure I knew what I was talking about. Not up for that, I just pointed out some of the more obvious things — that women basically didn’t use to have any rights, such as that to vote, so there sure as heck was a need for a movement for equality for women in the past. (There still is, but the reasons are less screamingly obvious.) Not being a total idiot, the other person saw this point, and next I saw him saying that feminism was needed in the past but is now dangerous since women now have more power. Still very wrong based on what I know, but not “The Earth is flat” wrong, and at least I made him think about it a little bit from a different perspective and come slightly closer to the same page with those of a different opinion.
Obviously, this won’t always work. Sometimes people just seem to act incredibly stupidly and not listen to anything at all someone tells them. Just look at this compilation (if it’s real) of people thinking The Onion (which is a satirical site, meaning it publishes intentionally false news as a joke) is reporting real news, and sometimes not even listening when they’re told it’s a joke. It will work sometimes, though — and it’s all too easy for basically reasonable thinkers to get totally mistaken about something, so there’s hope of people listening.
Another way of looking at it is that when you take one issue at a time, at least people will know what’s being talked about and not confuse issues. That’s also all too common, and it also leads to the use of fallacies like the false dilemma. Being emotionally invested in part of one’s beliefs or attitudes about the issue could also lead someone not to listen to any disagreement if they confuse any disagreement as one about those attitudes — but they are not always, and that should be made clear. Clearing up the matter of what is being talked about can also help if you have the wrong impression about the other’s views, and, let’s face it, that happens too.
It’s often possible and useful to make someone stop being “flat Earth” wrong, even if you can’t make them agree with you about everything. This potentially makes people think about things a little and understand them a little better, so it’s worth it. Or, you might just see someone being absolutely wrong and get an urge to correct — and this might be your best bet at succeeding in that.