So, I'll take this from a slightly different angle than some of the other folks. Let's say that your conversation partner is verifiably wrong, and you know it. Before chiming in to correct them, ask yourself how much goodness you're bringing into the world by doing so, and who benefits from your efforts to educate.
If somebody is telling a teenager learning to drive that gas is on the left and brake on the right, they may actually hit something before they learn it. It's okay to correct that information.
If they just use "poor grammar," mislabel some technological item they are not attempting to use in a professional capacity, or they're off by an order of magnitude on some statistic they're using as trivia to bolster an otherwise reasonable claim, then correcting them doesn't advance the conversation or meaningfully facilitate communication. It's just making them look and feel stupid and small to your benefit. While your conscious impulse was probably not cruel, the whole activity is also tied up with ego and impulse control: we all want to look smart and scratch that psychological itch to share what we know. You won't always be able to resist or agree that something is trivial, but you have to put in the effort.
As a chronic know it all now raising another one, I try to ask myself, "if I weren't able to speak right now, would I still think it was important to catch up with this person later and educate them?" If the answer is "no," then there's no need to step in right then either. I will also say that if you've surrounded yourself with people who care about you, they're going to tolerate a certain amount of it as a harmless foible, and they probably will use you as a resource when they think it's appropriate. In a way that makes me all the more determined not to abuse the goodwill of my friends and loved ones by being an exhausting pedant.
...except for Anti-Stratfordians. They can fuck right off. I've picked that hill to die on and until I do I will leave the bloodied corpses of a million potential friendships in my wake. Fortunately it doesn't come up often. 🤣
"The price of being right" enters into this as well. It can be very frustrating when you let something go because the minor details do not matter, but being 100% technically correct has hazards of its own in a social narrative.
Was watching the wire the other day and there is this whole scene where the Judge Phelan is being a pedant just to be a dick to McNulty. In the scene he is explaining the difference between then and than while insulting Jimmy the whole time. Its a really good scene of showing how people use pedantery to show status and shame others.
Aargh. My browser just wiped the long version. SHort version: People who think Shakespeare didn't write his plays and poems. They're virtually all classist assholes who think only a noble with an Ox-bridge education could write that well, completely ignoring what made Shakespeare different, the historical context in which he lived, how his reputation evolved over time, and how all of that is more than reasonably well-aligned with what we know about him.