> Toddlers (which includes defensive bureaucrats, bullies, flat earthers, folks committed to a specific agenda and radio talk show hosts)
If you've already decided your peer is a "toddler", correctly or incorrectly, you're definitely going to struggle to have any meaningful kind of dialog, that's for sure.
> If you’re not changing your mind, it’s likely you’re not actually having an argument (or you’re hanging out with the wrong people.)
Well, why do people argue in the first place?
Ultimately, it is probably something along the lines of "to spread one's own opinion", a cause not particularly noble in and of itself. Still, it is probably necessary. Most people are not aware of how seriously one's own perception is subjective; it feels like human nature, yet it's apparent if you look across enough people and enough culture that almost everything about our perception of issues is strongly impacted by culture, down to the language we use (though to be clear, I am not a believer in force-feeding the euphemism treadmill; fixing problems you manufactured isn't a net win for anyone. But I digress.) With that in mind, I think the importance of argument is apparent.
On an individual level, we have issues important enough to us, that we have formed opinions on. When we hear or see an argument that we disagree with, sometimes we feel enticed to debate it. In a public space, it's often more a performance than it is an actual argument between two people, but it's still an argument at its core.
In truth, there is not that much to gain from most arguments as they boil down to people who actually believe the same things but have a different framing of the situation, leading to a different outcome. You might change someone's mind by arguing with them, but only if they are both factually wrong about something and have the humility to admit it (and I think it is genuinely hard to sometimes, humans are just like that.) If they see the same exact factual information and have a different viewpoint, the real argument is one of trying to demonstrate which viewpoint holds more water. That's the real difficulty.
I don't really wind up having a lot of private one-on-one debates with people anymore. The reason is not because I don't want to grow or learn, it's because I've had a lot of debates about the issues most important to me and I feel like I understand the opposing viewpoints enough. I don't agree with them, but not because I can't figure out how someone could justify it.
Granted, there are viewpoints that I have an explanation for that I think holders of those viewpoints would not find to be particularly charitable, but that's not my modus operandi and I do adjust this when possible. In a lot of cases, e.g. abortion, gun rights, fiscal policies, I can see fairly reasonable arguments going different ways, and it often depends on what things you think are most important. This even extends to stuff that is less controversial that I have strong opinions on, like privacy rights and cryptography. The less charitable views are mostly reserved for the kinds of silly arguments you find spreading primarily from one moron to another, like conspiracies, or anything driven primarily by outrage bait.
I can see why you wouldn't argue with those people, but personally I think there are cases where you should. Ultimately, I think public debate is better than the ominous viewpoint suppression systems that modern social media deploys. (In many cases, both are worse than simply having reasonable moderation that can make subjective calls.)
Ultimately, I don't really think conspiracy nuts are toddlers or especially emotionally immature. I think a lot of them feel a disconnect from society and a distrust of authority, and find connection and possibly even a weird sense of security from conspiracy theories. Sometimes having someone to blame and grand explanations for why things are the way they are just makes us as humans feel better. But should you argue with them? At the very least, probably not for your sake or theirs, but maybe for other people's sakes sometimes.
Or maybe even more, it might be worth asking what it really means to "win" an argument. Changing the other person's view is not the definition I'd go with.