It's a good article in a lot of ways, and provides some warnings that many neural net evangelists should take to heart, but I agree it has some problems.
It's a bit unclear whether Fchollet is asserting that (A) Deep Learning has fundamental theoretical limitations on what it can achieve, or rather (B) that we have yet to discover ways of extracting human-like performance from it.
Certainly I agree with (B) that the current generation of models are little more than 'pattern matching', and the SOTA CNNs are, at best, something like small pieces of visual cortex or insect brains. But rather than deriding this limitation I'm more impressed at the range of tasks "mere" pattern matching is able to do so well - that's my takeaway.
But I also disagree with the distinction he makes between "local" and "extreme" generalization, or at least would contend that it's not a hard, or particularly meaningful, epistemic distinction. It is totally unsurprising that high-level planning and abstract reasoning capabilities are lacking in neural nets because the tasks we set them are so narrowly focused in scope. A neural net doesn't have a childhood, a desire/need to sustain itself, it doesn't grapple with its identity and mortality, set life goals for itself, forge relationships with others, or ponder the cosmos. And these types of quintessentially human activities are what I believe our capacities for high-level planning, reasoning with formal logic etc. arose to service. For this reason it's not obvious to me that a deep-learning-like system (with sufficient conception of causality, scarcity of resources, sanctity of life and so forth) would ALWAYS have to expend 1000s of fruitless trials crashing the rocket into the moon. It's conceivable that a system could know to develop an internal model of celestial mechanics and use it as a kind of staging area to plan trajectories.
I think there's a danger of questionable philosophy of mind assertions creeping into the discussion here (I've already read several poor or irrelevant expositions of Searle's Chinese Room in the comments). The high-level planning, and "true understanding" stuff sounds very much like what was debated for the last 25 years in philosophy of mind circles, under the rubric of "systematicity" in connectionist computational theories of mind. While I don't want to attempt a single-sentence exposition of this complicated debate, I will say that the requirement for "real understanding" (read systematicity) in AI systems, beyond mechanistic manipulation of tokens, is one that has been often criticised as ill-posed and potentially lacking even in human thought; leading to many movements of the goalposts vis-à-vis what "real understanding" actually is.
It's not clear to me that "real understanding" is not, or at least cannot be legitimately conceptualized as, some kind of geometric transformation from inputs to outputs - not least because vector spaces and their morphisms are pretty general mathematical objects.
EDIT: a word