Why do academics tend to be reluctant to ask for help from other academics? I've seen situations like the below happen quite a few times.

Alice writes a paper. It's well-received and receives a hundred citations. Bob also works in the area, and he engages a student Charlie to study the paper. Shortly after starting, Charlie tells Bob he couldn't get from equation 10 to equation 11, in fact he thinks the derivation is incorrect. Bob is incredulous (after all the paper is well-received and has a 100 citations) and tells Charlie to check it again. A few weeks later, Charlie tells Bob he still can't get equation 11, and in fact he's increasingly convinced the derivation is wrong because he's tried it in a few different ways and always gets the same result.
Bob starts looking at the paper himself and after another few weeks he also runs out of ideas. Finally they write to Alice asking for details. Alice responds quickly with, &quot;you've made this mistake. After correcting it and making this transformation, equation 11 follows.&quot;

The specific details vary, but the core of what happens is the same: Bob and Charlie can't do what Alice has done, but instead of asking Alice for help, they insists on trying it themselves. After weeks of struggling and many tins of coffee, they finally give up and ask Alice, who proceeds to solve the problem very quickly.
The question: why would Bob and Charlie grind away for weeks when help is just an email away? If I managed a team of employees who refused to ask each other for help, especially when someone has already solved the problem, I'd be quite annoyed. After all, time is precious.
I find this especially surprising because virtually every professor I've seen teach encourages their students to ask questions. Instructors tell their students they're welcome to interrupt during class, to approach TAs, or to visit them during office hours. They discourage their students from working without progress for weeks before asking for help, and yet they're reluctant to ask for help themselves. Why?
The only reason I can think of is that Bob and Charlie want to be sure that the results are robust. If Alice made a mistake, then they would not be able to duplicate the results, but if they just ask Alice for help, then they're at risk of making the same mistake. But this doesn't seem like a strong reason: they can ask for help but then critically examine what Alice says.
I have never been fully immune from this kind of behavior, though I've suffered less from it than others, a fact that most likely helped me land two really nice jobs. Let me survey a few reasons why I think it happens.

Note: I'm talking of mathematics, where "robustness" is not a thing, and talking to someone does not "contaminate" your thinking (unless you are really careless).


Bob and Charlie are too proud. They don't want to be seen asking possibly stupid questions in writing.
Charlie feels that he doesn't know enough to even pose a good question, and Bob doesn't care enough. (Students generally tend to have trouble gauging their level, and I have occasionally blundered into conversations I wasn't prepared for by asking a too-advanced question.)
Bob and Charlie have seen their questions ignored too often. (My personal experience is that the usefulness of emailing an author about a paper they wrote declines sharply with the age of the paper. If the paper is 15+ years old, they most likely don't remember anything and have the same perspective as any other reader.)
Bob and Charlie don't want anyone to know they are reading the paper, as they are worried of creating expectations. (This sometimes does happen -- in that an author takes a question as a stronger sign of interest than it was intended. Though it does not appear to be a big deal, but more of an awkward moment.)
Bob and Charlie are worried Alice will view their question as a personal attack or at least as a threat. (In my career of reporting errors, this has happened 1-2 times out of somewhere near 50. But this sort of risk aversion isn't exactly out of character for much of academia...)