To know what I am talking about, let me give you an example. I have this friend who went crazy over the vaccine issue. She's done so much research into it that I feel like I can't talk to her about her vaccine skepticism. Whenever I start to talk about something, she would drown me with a ton of articles and youtube videos and most of the times from the actual websites of UN health and stuff. It would have taken me a day to just go through that stuff. So I gave up on convincing her about vaccines. Might seem cruel but even I lost my certainty about vaccines after I met her. There's just too much to know and I don't completely trust the institutions either, but I do trust the institutions enough to vaccinate myself and my kids but not enough to you know, hold a debate about it with someone who has spent days researching this stuff.
You can take any topic which is divisive, which basically looms over the media all day and you can find a ton of articles to either support it or "debunk" it. I think 9/11 wasn't caused by Bush, I am almost certain, but I won't bet my house on it. I mean, this is almost a certainty, but yeah.
On other issues which are not this much of a certainty I fail to see how to convince a person who thinks something that they are wrong.
Stuff like earth is round or not, I can prove. But was the virus from Chinese market or from a lab, I can't.
Have aliens visited earth? I don't know. It would be wicked if we make first contact, but as awesome as this is, I am not motivated to search about this on the internet. I don't think I would search anything about the not so cool topics of life. I don't know enough to hold an informed debate about capitalism vs socialism or any other hot button issue for that moment.
What do you do in these situations?
I can sense that this is poorly written, but I hope you get the gist of what I am trying to say.
The core issue is ignorance and and poor abilities at investigation. School fails so many people. And, societally, most people seem to feel they're entitled to opinions even if they know nothing or very little about a topic, which helps keep them ignorant and unable to critically investigate topics and sources.
Finally, the "trust in institutions" issue. These institutions should not be trusted, they have been overtaken by capitalism. Healthcare is profit-driven and the tendency is towards poorer science that covers up dangers and inflates benefits. In addition, people have no sense of agency over the state (they're correct about that), so a feeling of understanding can temporarily substitute that.
The question is what to do about it. Well, individually, you can do very little. You can try to convince people through argumentation, like you mentioned, but this is very difficult. The example of vaccines makes it clear that this is someone that bought into these ideas without critically engaging. They probably did so for a number of reasons, including societally-ingrained hubris, peer pressure, personal experience, personality, politics, and the production value of whatever got to them first. Your task is to sow doubt (ask challenging questions) and try to rebuild from shared understanding.
The best way to combat this, more generally, is not as an individual, but as a member of an active organization that combats all of this at once, and with a plan for how to do so adequately. This would best be a socialist org, as the thing you're fighting is actually the discursive mass media and education aspects of capitalism. e.g. on COVID's origins, the common understandings and claims in the West are simplistic and unscientific, and only exist for political reasons, to scapegoat why a given country did so poorly at handling the pandemic, to isolate China in a new cold war. You could become an expert in the science, follow geographic phylogenies and the terminology of epidemiology, but you don't really need to: you really just need media criticism skills, which is all about politics, economics, and being a big nerd.