Consider the problem of an agent who is offered a chance to improve their epistemic rationality for a price. What is such an agent's optimal strategy?
A complete answer to this problem would involve a mathematical model to estimate the expected increase in utility associated with having more correct beliefs. I don't have a complete answer, but I'm pretty sure about one thing: From an instrumental rationalist's point of view, to always accept or always refuse such offers is downright irrational.
And now for the kicker: You might be such an agent.
One technique that humans can use to work towards epistemic rationality is to doubt themselves, since most people think they are above average in a wide variety of areas (and it's reasonable to assume that merit in at least some of these areas is normally distributed.) But having a negative explanatory style, which is one way to doubt yourself, has been linked with sickness and depression.
And the inverse is also true. Humans also seem to be rewarded for a certain set of beliefs: those that help them maintain a somewhat-good assessment of themselves. Having an optimistic explanatory style (in an nutshell, explaining good events in a way that makes you feel good, and explaining bad events in a way that doesn't make you feel bad) has been linked with success in sports, sales and school.
If you're unswayed by my empirical arguments, here's a theoretical one. If you're a human and you want to have correct beliefs, you must make a special effort to seek evidence that your beliefs are wrong. One of our known defects is our tendency to stick with our beliefs for too long. But if you do this successfully, you will become less certain and therefore less determined.
In some circumstances, it's good to be less determined. But in others, it's not. And to say that one should always look for disconfirming evidence, or that one should always avoid looking for disconfirming evidence, is idealogical according to the instrumental rationalist.
Who do you think is going to be more motivated to think about math: someone who feels it is their duty to become smarter, or a naive student who believes he or she has the answer to some mathematical problem and is only lacking a proof?
You rarely see a self-help book, entreprenuership guide, or personal development blog telling people how to be less confident. But that's what an advocate of rationalism does. The question is, do the benefits outweigh the costs?
Reversing stupidity is not the same thing as swerving an arbitrary amount in the right direction. And the amount is not arbitrary: like most of my belief changes, it is based on my intuition. This post by Robin Hanson springs to mind; see the last sentence before the edit.
Anyway, some positive thoughts I have about myself are obviously unwarranted. I'm currently in the habit of immediately doubting spontaneous positive thoughts (because of what I've read about overconfidence), but I'm beginning to suspect that my habit is self-destructive.
Well yes, of course, it's easier to do something if you believe you can. That's what I'm talking about--confidence (i.e. believing you can do something) is valuable. If there's no chance of the thing going wrong, then you're often best off being overconfident to attain this benefit. That's pretty much my point right there.
As for your Heinlein quote, I find it completely unrealistic. Either I am vastly overestimating myself as one of Heinlein's elite, I am a terrible judge of people because I put so many of them into his elite, or Heinlein is wrong. I find it ironic, however, that someone who read the quote would probably be pushed towards the state of mind I am advocating: I'm pretty sure 95% of those who read it put themselves somewhere in the upper echelons, and once in the upper echelons, they are free to estimate their ability highly and succeed as a result.
Are you in the habit of immediately doubting negative thoughts as well? All emotionally-laden spontaneous cognitive content should be suspect.
Also, when you correct an overly positive self-assessment, do you try to describe it as a growth opportunity? This violates no principles of rationality, and seems like it could mitigate the self-destruction. (See fixed vs. growth theories of intelligence.)