He gives several examples of poorly-written FP code (which we're supposed to believe is "clever" by virtue of being FP), then introduces some new problem constraint which is carefully selected to make the FP solution break but some equally ridiculous imperative-style code not break. In fact, what he really wants to say is, "FP is stupid", but he won't come out and say it.
This is illustrated perfectly by the curve-fitting analogy: a perfectly-fit 5th degree polynomial is the "clever" solution, but oh wouldn't it be so much simpler to use an best-fit 3rd degree function? And oh look, the 3rd-degree polynomial has a positive slope at the end whereas the 5th degree polynomial has a negative slope, ergo if we just happen to pick a point greater than the previous one, ta-da! The 3rd-degree polynomial fits the new set better than the 5th-degree. QED.
When put that way, the argument is completely idiotic. You could just as easily have picked a new point lying, say, on the 5th-degree polynomial and thus "prove" that it was a better fit for some yet-to-be-defined data than was the "non-clever" 3rd-degree polynomial. The analogy to the code is that it would be trivial to come up with new requirements which could be easily solved by the "clever" FP code and very difficult by the imperative-style code; and in fact the author admits as much in the second case.
By the end I can't help but wonder if this was satire, designed to make anyone agreeing with the article look silly when the author later comes out pointing out all the above...