There's a Fallacy called the Fallacy Fallacy which is a Fallacy that's based on the idea that if an argument has a Fallacy the conclusion is false which is a Fallacy, the Fallacy that the Fallacy Fallacy is about.
Given how often I encounter someone linking a fallacy and saying my argument is thus and feels they have now won I can see it. Many times to the only evidence of my argument being the fallacy is their own opinion. I will often ask them to back up why it is the fallacy and I get the usual dude if you don't get it thats your issue. Im guessing to that I likely have more experience with philosophy, logic, and debate than these folks. But yeah this touches on a thing with me because they don't seem to get that fallacies are the effect of wording more than anything else.