Why are so many smart people idiots about philosophy?

Aside from the general points in other comments as well as the article itself, I would contend that even modern philosophers are ignorant of real and abiding philosophy.

The contemporary conception and definition of philosophy, of what it is about and its methodology, is directly related to the misinterpretation and misunderstanding of the approach adopted by some of the well-known ancient Greek philosophers from their public works. From this error of conception and approach, over time a solely intellectual approach has been developed by the modern pseudo-philosophers with their equally pseudo-philosophy. Academia has never truly understood the real nature of philosophy.

As for science, well a similar paradigm exists for it in its proclivity to be defined and developed around a partial representation of what it means and should be, from the point of human concepts and its bias. In other words, it's been defined entirely from one philosophical perspective of life and its methodology oriented around that restrictive perspective. This is the reason that, until science itself learns to extend their perspective and conceptual viewpoint, it will never arrive at real causes or origins but rest on mere effects.

If "smart person" is a proxy for "scientists and engineers", the answer seems obvious; it's not included in their education.

Not in primary school, not in secondary school, not in their major, and not in graduate school.

If people truly believed in the importance of "smart people" learning about philosophy, they would put more effort into making sure they were actually taught some at some point.

The ignorance of philosophy among educated people is a relatively recent phenomenon. It happened in part because the American philosophical community after WWII shifted away from pragmatism and adopted a type of philosophy, namely analytic and logical positivist, that is quite counter-intuitive and also quite irrelevant to most real problems in the world.

To paraphrase whoever said it originally about Stephen Fry 'Nye is a stupid persons idea of what a smart person is'.

A 'truly smart' person wouldn't dismiss an entire discipline out of hand simply because they don't know anything about it, especially not philosophy which is arguably the 'mother' of all science.

I do think it should be a part of basic education, philosophy and programming are two skills that really teach you to think and will last a lifetime.