This stood out to me especially because of the word 'fragile' applied to know. I've used that word too, but I've never heard it done anywhere else. My idea (which is probably due to David Deutsch or to Kolya Wolf) can be explained a couple different ways.
One manifestation is that if someone is really interested in something, when they learn it, and they think about it a lot, then they will understand it in depth, and from lots of different angles, and they will figure out how to use it in lots of different ways, and they will integrate it with all the other things they know, so it plays a useful role in their overall way of thinking about the world. That's knowledge that *isn't* fragile, it's robust. Towards the opposite end of the spectrum is when you learn something the day before a test, and just try to remember the exact question that is likely to be on the test, and the answer. If you learn it like that, you'll probably forget after a couple days, and you never learn how to apply the idea to other issues -- that's fragile knowledge. I call it 'fragile' because it breaks very easily. You just change the problem situation a little and suddenly it stops working. It's not robust.
One way fragile knowledge gets created is when people are forced to learn something. Maybe you can make them learn the specific answers to the exact questions you ask, if they are scared enough of displeasing you. But that's never going to make them think about it, on their own time, for fun, and integrate the ideas into their personality, and make it a part of how they see the world. Quite the opposite. They are going to have really bad feelings attached to it, and avoid it when they can, and not see any of the ways to apply it to more of life.
Another way fragile knowledge gets created is when people do work purely for the money. Then they solve the exact problem their employer wants solved, and that's it, and they don't think about how they could use the stuff they are doing in more ways, cause they only care about the money and not the knowledge.
Another idea is that this connects to structural epistemology, and different knowledge structures can be more or less fragile. Almost no one knows what structural epistemology is, except computer programmers, but they aren't philosophers, so they don't know what epistemology is, but they do understand the idea. So when I give examples of knowledge structure, I usually give programming examples, cause it's the only field where people know much about the difference between different ways of structuring the same knowledge, and discuss it all the time, and even write books about it. So let's say you want a program to add up 2+2 for you. Now one way you could do this is write a calculator program that can add up any numbers, and also multiply and do other operations. Then it can add up 2+2, but it's also robust, it can add up 3+3, and all sorts of other numbers. It has knowledge in it that lets it apply to lots of questions besides just 2+2. Now suppose you wrote this program:
It's a lot more fragile. When you want to add 3+3, you need to write a new program. This old one is no good. It can't solve any other problems except 2+2. It's not adaptable to other situations except the exact one its designed for. So it's just like studying only for the test tomorrow, and what you learn isn't adaptable to any other situations. Of course, this fragile program is really easy to write, so sometimes it's good enough. The point isn't the fragile way is always worse. But it's different, and it is *fragile*, and it's a good thing to be aware of. And for a lot of people, most of their knowledge of the world is fragile, and that's a big problem! Some people never create much robust knowledge, and that's sad.