When I mentioned the model not matching reality, that's basically the same thing as saying your assumptions are incorrect. That's the fatal flaw of logic: you can't really use it to model the real world without making tons of assumptions about how the world works. For instance, technically speaking, science as a whole is illogical. If 9 people who jump off a roof fall to their death, there is no purely logical reason that the 10th person to jump won't fly instead.

As to "an example of constructing a logical argument that proves something that isn’t true" I'm going to be a bit pedantic here and point out that I said

It’s possible to construct logical arguments that “prove” things that are untrue

And draw attention to those quotes. You can construct a logical proof, but that doesn't mean that actually says anything about the world. What I'm meaning is when someone uses a logical proof to claim something untrue is true.