If you're in the sky and you want to stay there, you have to counteract gravity. Heavier-than-air flight does this by pushing down on air. Want to stay in the sky? Push down on enough air, fast enough, and you will stay in the sky.
Since air is a fluid, pushing down on air is equivalent to pushing air down. The lift a plane or helicopter generates is directly proportional to the amount of air it pushes down (and to a varying degree how much engine exhaust it pushes down). That is, we need something to divert air downwards and something to push us through that air. The better we can redirect air downwards, and push ourselves through the air, the easier it is to fly.
We have found many shapes that are very good at passively redirecting air when pushed through the air, we have developed engines that are good at pushing us through the air, and we have developed structures that are able to hold everything together while being light. That is why heavier-than-air flight is possible, and it's very well understood.
If anything, our understanding of why certain shapes redirect air so well is lacking, but even then not really. Experiments and modelling are really good at finding the conditions under which air stops being redirected efficiently. If we try to parameterise this airflow, and reduce it to simple equations, well maybe then the effect is not well explained. Statements like "the air moves faster on the top than on the bottom, so there is a pressure differential and hence a lifting force" may be true even if misleading, and statements like "the air moves faster on top because it is longer than the bottom side" are definitely misleading and incorrect, but just because these statements exist and some people believe them does not mean we don't understand heavier-than-air flight! Such flight is possible because we are able to push down on air with enough force to keep us flying, and so much of how that works is well understood.
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To try and say something directed more at the point the article seems to be making: confusion or misunderstanding about the technical details, or modelling, of something is very different to not understanding how that thing works.
We understand heavier-than-air flight in the exact same way we understand sailing - redirect airflow to generate a force for your own purpose - but you don't see articles about how we don't understand how sailing works.