Several things will help us here. First, the paragraph functions much better in context. It's in a technical discussion of rhetoric, and it helps to know that for reasons I'll get to in a moment. Second, there's some grammatical errors, which I'll point out. Third, this is clunker of a paragraph, so a useful approach to detangling it is to prune it.
Rhetoric: in rhetoric there are multiple "arguments" being discussed at once. There's the primary argument of the proponent, and then there's the (counter) argument criticizing the original argument. Labeling something a fallacy is a tactic in counter-argument, that says "the primary argument is bogus". This discussion? Is about whether or not using the fallacy under discussion is a logically valid rebuttal of an argument that is itself a counter-argument. Yes: this paragraph is taking a side (i.e. propounds an argument) in a discussion (also called an argument) as to whether the fallacy is a good counter-argument against an a counter-argument against an argument. Yes, an argument as to the validity of an argument against an argument against an argument.
You haven't got a prayer of parsing the second sentence of this paragraph without knowing that fact.
Grammar: The first sentence reads:
This fallacy, like most (with the exceptions being fallacies of formal logic like affirming the consequent and denying the antecedent), are not however absolute nor are they strict.
That's wrong. The subject and the verb do not agree in number; neither does one of the pronouns. This is apparent if we flense out the irrelevant parentheticals:
This fallacy are not absolute nor are they strict.
It should clearly be:
This fallacy is not absolute nor is it strict.
Now we're getting somewhere.
Let's continue cutting this monster down to size:
By saying they are not strict, I mean merely being able to point out that something can be called a fallacy does not mean that you are not identifying a valid problem with an argument.
Okay, consider just the first part:
By saying they are not strict, I mean
Everything that happens after that, in that sentence, has to be able to stand on its own as a valid sentence, so we can slice this right off the front of it. That gives us:
Merely being able to point out that something can be called a fallacy does not mean that you are not identifying a valid problem with an argument.
Now we're getting somewhere. Time to apply that fact about what sort of discussion about rhetoric this is.
The context for this paragraph is a discussion "Is it fallacious if someone does the following thing in their counter-argument?"
The upshot of this double-negative sentence is, "Maybe, but that doesn't necessarily invalidate their counter-argument."
Part of why this is unclear is the imprudent choice of the author to use the pronoun "you" instead of something less ambiguous. "They", even, would have been better. Everybody in this discussion, both real participants and hypothetical discussants, has an argument. Which argument are we talking about?
It helps to list them out:
Argument 1: blah!
Argument 2: Not blah! Because reason 1! Argument 1 is defeated!
Argument 3: Not reason 1, because reason 1 is a rhetorical fallacy! Therefore not not blah! Argument 2 is defeated and Argument 1 stands!
Argument 4 (THIS DOUBLE-NEGATIVE SENTENCE): Well, no. Not "not reason 1", because, while yes, it is a fallacy, something being a fallacy doesn't necessarily invalidate it as an argument. So it's wrong to claim Argument 2 is defeated because reason 1 is wrong; reason 1 can be wrong but Argument 2 still be right. I.e. Argument 2 can, despite being a fallacy, still be a valid rebuttal of Argument 1. So Argument 3 is defeated, Argument 2 stands, and Argument 1 is still threatened by Argument 2.
I have no idea if I'm being helpful at this point, so I'm going to stop.
