I think it's common for highly-intelligent (not solely as an IQ measure, but maybe a dash of that plus a high level of self-awareness and emotional intelligence) to consistently rate themselves below average, and for a lot of people with deficits in all three categories to do the exact opposite. I think the main reason is that people who are challenged in these areas don't have as many 'known unknowns" (not being remotely aware of the knowledge gaps and even biases they hold), and people with a higher capacity for learning can often pinpoint all of the things they actually don't know in great detail, and feeling very small in comparison.
It's not an absolute science, but whenever someone says, "I'm very smart!" I usually assume it's coming from a point of view of extreme stupidity or possibly even some form of narcissism, because while we may have some great areas of expertise on an individual level, something is inevitably going to slip through the cracks, and thus people who are aware of this are always going to feel a little bit dumber by nature.