Intelligence in the intellectual, logical reasoning sense is a evolutionary epiphenomenon. It is only weakly selected for. We can tell this because its distribution in the population is so broad. There are no gazelles that run at half the speed of the fastest[*] but there is no shortage of people with IQs that are half the top and still manage to get along (putting "the top" at around 160 and "the bottom" around 80, which is the lower end of the "gets along OK in society most of the time" range.)
Logical, linear reasoning is a trick we've managed to train our bear to dance.
Some people happen to be really good at it. This can be a problem for them because so much of what humans do, and the accounts they give of it, make very little sense to the untutored mind.
We live in the Age of Bayes, and the Bayesian Revolution over the past thee hundred years (which takes in a lot of time before Bayes himself or the recognition that what we were doing is fundamentally Bayesian) has taught us some really important lessons about ourselves. Mostly how damned stupid we have been, even the highly intelligent. We've spent centuries arguing nonsense, from how three is equal to one for large values of three to the dharma of the tao.
In the past century or so we've been calling out the people who are most "intellectually gifted" and expecting them to solve our problems (in a past age it was the pious, or the people "of good family", etc). This has created a bind for them, because for most of that time we've also had no idea why people do what they do (spoiler: mate competition and selection play large roles, although we are still a long way from any kind of comprehensive understanding.)
There are also ethical constraints on what can be done to solve human problems. The utopian projects of the 20th century, despite their profound irrationality in so many respects, were manifestations of this belief that the human intellect had all the right tools for the job of reforming the planet. It didn't work, and that leaves us in the situation we are in today, where intellect is suspect as well as desired.
As such, it isn't necessarily a shock that people identified as "intellectually gifted" should feel less adequate after exemplary lives. Nor is it likely that's going to change any time soon, as we continue to look to the intellectually gifted to save us from ourselves, while steadfastly refusing to spend any time looking hard in a mirror for the source of most human problems.
[*] this may be false... feel free to fact-check me!