It seems to me that you are mixing up two questions. One question is why your mentees study things they think are neither interesting nor important. The other question is why people might be encouraging them to do so. For the first question, why don't you start by asking them? I'm not claiming that they'll have perfect introspection; in particular, I don't expect them to admit to 5, but if the reason is 1, I do expect them to articulate that. But I don't expect many people are motivated by 1; that seems more like the answer to why Amy Chua wants her children to do things. And even if the children know that it reflects parental desires, they may not be able to explain the parental thinking.
Also, to the extent that your goal is to explain the survey, in particular the frustration, I think you can rule out 2 and 4 and maybe 3. Those of 2 and 4 would just move on to another subject.
Another way to put the two questions: why do people do this; and why should people do this?
A priori, it seems to me that one should engage in activities only if they satisfy at least one of these two conditions:
But investigation we did in connection with our research at Cognito Mentoring led my collaborator Jonah and me to notice that a fair number of people seem attracted to learning things for the sake of learning, although they neither have an internal belief that learning the subject is important, nor a deep interest in learning that specific topic. Some of them then get frustrated that they're unable to make progress on their self-set learning goals, and this may harm their self-esteem (and put them off learning more important things later). Others may experience success that encourages them to learn more things, some of which may be interesting or important. Our page on managing your time generally advises against participating in and focusing on such activities, or at minimum critically considering whether the activities are sufficiently important to justify engaging in them even if one doesn't find them interesting.
However, Jonah and I may be missing important perspectives. I've heard claims that engaging in activities that are neither interesting nor important has intrinsic value -- it helps build character, makes one grow as a person, or it just might turn out to be important.
This school of thinking is reflected in diverse quarters. Tiger Mom Amy Chua famously forced her daughters to learn musical instruments to build their character, even though at least one of her daughters found it a terrible experience, and there was no reason to believe that the activity itself is important. The belief that one should try and learn new things is also widespread (albeit in a very different sort of way) in the rationalistic self-help community.
What's going on? Some possible explanations:
What do you think?