Because they are autodidacts.  The main purpose of higher education
  and making all the smartest kids from one school come together with
  all the smartest kids from other schools, recursively, is to show every
  smart kid everywhere that they are not the smartest kid around, that
  no matter how smart they are, they are not equally smart at everything
  even though they were just that to begin with, and there will therefore
  always be smarter kids, if nothing else, than at something other than
  they are smart at.  If you take a smart kid out of this system, reward
  him with lots of money that he could never make otherwise, reward him
  with control over machines that journalists are morbidly afraid of and
  make the entire population fear second-hand, and prevent him from ever
  meeting smarter people than himself, he will have no recourse but to
  believe that he /is/ smarter than everybody else.  Educate him properly
  and force him to reach the point of intellectual exhaustion and failure
  where there is no other route to success than to ask for help, and he
  will gain a profound respect for other people.  Many programmers act
  like they are morbidly afraid of being discovered to be less smart than
  they think they are, and many of them respond with extreme hostility on
  Usenet precisely because they get a glimpse of their own limitations.
  To people whose entire life has been about being in control, loss of
  control is actually a very good reason to panic.

–– Erik Naggum, 2004

Good ones don't... just like any field...

"Intelligent" people know how much they don't know... "Stupid" or "ignorant" know everything and want you to know it.

Doctors, Mechanics, ... nerds... no one group is immune to this.

https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effect

"The Dunning–Kruger effect is a cognitive bias in which low-ability individuals suffer from illusory superiority, mistakenly assessing their ability as much higher than it really is. Psychologists David Dunning and Justin Kruger attributed this bias to a metacognitive incapacity, on the part of those with low ability, to recognize their ineptitude and evaluate their competence accurately. Their research also suggests corollaries: high-ability individuals may underestimate their relative competence and may erroneously assume that tasks which are easy for them are also easy for others."

I thought the most interesting aspect of these studies is that intelligent people are better at judging the intelligence of others. Those in the bottom quartile could not estimate the intelligence of peers much better than random chance. Those near the top could estimate the intelligence of others with high accuracy.

This has profound implications in hiring selection. Having exceptionally bright founders could cause a.... founder effect resulting in the entire company being much smarter than average.

Anecdotal, but I know of quite a few wildly successful companies where the founder/CEO still participates in all interviews despite having more than a thousand employees. This seems like a random company quirk but, taking this research to practice, could actually be a large part of why these companies are successful.

With warning of anecdote rather than evidence, Doctors are the worst [1] for this! So many of them seem to think they're scientists, when the majority of them are far from it.

[1] In the hyperbolic sense; I wouldn't like to suggest a literal truth here

Doctors are at a bad intersection of customer service and science.

On the one hand, doctors need to sound authoritative to 99.9% of all people since they are almost always delivering news the patient doesn't want to hear (exercise, eat less junk, take these pills 3 times equally spaced not 2 with lunch, etc.)

On the other hand, many doctors just aren't that smart. Being a doctor today isn't an automatic sign to me that you are in the top 1% of brainpower. Some of my doctors are, most aren't. In addition, many doctors don't continue to learn over time. If you do that, you eventually become dumb.

Well if you listen to doctors they'll say we apply scientifically proven methods, and some portion of them actually do science. My impression is that doctors like to sound smarter than they often are. Since medicine is more of an art form than anything - most physicians are like artists (albeit highly trained ones). And as with any art you have the whole spectrum of quality.