I think its portrayed in a way that makes it seem larger than it is. These types of mysteries exist all throughout engineering and physics. Its rightly stated, imo, that math is not an explanation in itself, just like theories (especially incomplete ones) are not answers.
The bare fact is that "we" do know what makes planes fly. The answer is "lift", and we have been using equations to build aircraft that can manipulate, create, and destroy lift for more than a century. The article does a bait-and-switch with the question, and tries to say that "yeah but what is lift" is a continuance of the question, when its in fact another issue entirely. Every matter is eventually reduced to "we don't actually know" if you repeatedly ask "why" until you get down to the bottom of the well. Which is actually fine, its just that some people (often people steeped in science) get really upset when faced with this reality.
This is why I brought up Unified Theory, which probably if one tries hard enough one can tie all scientific uncertainty back to. There aren't any final answers, but that doesn't mean its accurate to say "we don't know how planes fly" just because we don't know how to rectify classical and quantum physics.
"We have several theories about what causes lift but there is still more to discover" doesn't make a snappy click-bait title though.