Okay! So. A bit more on those two ideas.
Somewhat paradoxically, the two biggest influences on my thought and reasoning processes are my career as a HS debater and my mediation training. And man alive, they have never seemed more relevant than today.
Re: the first one: I was a Lincoln-Douglas debater in high school. I strongly recommend doing this, at least for a year or two, for anyone who has the stamina, because it is GRUELING. But what it does is teach you, quite literally, how to argue; you can't win a debate without proving the "value" that you're arguing for to be superior, and you can't do that without having both facts that stand up to scrutiny and counter-arguments that anticipate and address your opponent's claims. That's not a strategic recommendation - that's a requirement. (If you don't successfully address your opponent's claims, no matter how ridiculous they are, they officially stand, which is a point against you.) As a result, you learn quickly to check your sources for bias and to ensure that the facts you offer aren't limited to one or two instances. Or you're hosed. That's just how it works.
Which is why it pains me so to see people in the current political climate repeating claims without having bothered to check their sources or the nuances of an issue. It's true on both sides of the aisle, and it bugs me mostly because it is the FASTEST WAY TO LOSE AN ARGUMENT, full stop. Even if you're correct, nothing undermines your credibility more than revealing that the same source that you're citing on healthcare policy also claimed that you could cure your cancer with magnets and a glass of milk.
One would think that this stands to reason, but all one has to do is spend some time on one's social media platform to realize that hysteria - and the sharing of questionably sourced articles - is easier to give in to than one might think. Even the best of us will rely sometimes on a heartrending story, but that story isn't very useful unless it's representative of a larger argument. (Repeat after me: THE PLURAL OF ANECDOTE IS NOT DATA.)
And I get that this is annoying and exhausting and stressful, particularly when you're dealing with people who don't feel the need to do the same (again, both sides). It doesn't seem like it should be necessary. But hell, it doesn't seem like it should be necessary for me to be telling you to check your facts, and here I am, writing this instead of doing something else, so.
However: there's a larger question about whether "winning an argument" is the framework we should be using at all for this. Which is where the mediation training comes in. (Don't worry, you're still going to need reliably-sourced facts for this.)
When I was in grad school, I took a training in order to become a court mediator. It's not an exaggeration to say that this training completely changed my way of thinking. The point of mediation is not to "win" per se; it's to come up with a mutually satisfying outcome for both parties. What that means, in practice, is that you have to understand what the other person wants, but more importantly, you have to understand why they want it and where that overlaps with what you want and why you want it.
There are probably a few people in the world who can see a completely different set of facts and say "Okay, you're right, I was wrong," but I don't know them. Most people, when they take a political stance, have a deeper driver that needs acknowledgment: I feel unsafe. I feel ignored. I feel overlooked or disrespected. Which is why just getting up and saying "Here are the facts, asshole" doesn't tend to work super well. It works in debate, of course, because there are judges there and pre-existing rules that everyone has agreed to abide by. But in life, and on Facebook, there's no one there to keep score and declare a winner.
So if you decide that you want to undertake the exhausting endeavor of getting someone else to agree with you, or at least disagree with you less, it's vital to acknowledge their concerns, EVEN IF YOU DON'T SHARE THEM. You don't have to share them to say "I understand that you feel that way." "I understand that you're concerned about safety." "I understand that you're worried about healthcare." And - I know this is crazy - TRY TO UNDERSTAND THEM. You're probably not going to agree! That's okay! You can at least use this as a metric to assess the arguments they present. And if you can find some common ground that way - "I am also concerned about safety, and can agree at least on X" - then the tenor of the argument has already gotten less vitriolic.
And this is where the debate training comes back in. Your facts still need to be credible. You'll be much better prepared to understand where they're coming from if you've anticipated the counter-argument, and who knows, you might even have found some facts to address their concerns. But - thanks to the mediation approach - you won't be dealing with someone anymore who finds it actively painful and humiliating to agree with you. You don't want to put people in that position. It doesn't work.
Of course, I'm something of a hypocrite in this regard, because I try to stay out of social media-based arguments; as noted, they're exhausting, and I find it more effective for me personally to direct my energy in this area elsewhere. And I should also note that you may still not win, because emotions and power make people unreasonable. You're not going to be able to come to a civil agreement with everybody.
But - call me naive - I believe that people can change, and that more people than not can be at least spoken with. Nonetheless, you can't engage at all if all your "facts" are yelled and come from some rando's Twitter feed. This is an annoying baseline to begin with, but we've got to start somewhere.
I will leave you with this graphic, which I think is hugely important. You may disagree with a few of the placements (particular apologies to my friends who work at and/or read USAToday and CNN - I don't think that's fair), but the overall idea, I think, stands up pretty well.