Have logical fallacies become too convoluted to the point of being self-defeating?

DrCereal

SnakesOfferingApples said:

I think that they could and have become self-defeating, an example of this can be seen in the definition of a logical fallacy - A logical fallacy is an error in reasoning that renders an argument invalid. If this is the definition then aren't all logical fallacies guilty of the Fallacist's fallacy? Which is basically the fallacy of not taking an argument seriously because it contains a fallacy.

I hope no one who mentions a fallacy immediately declares that the conclusion is false, but simply mentioning a fallacy that defeats the argument is not an argument from fallacy.