So you're saying most of the best frameworks are built off pain and struggle?

Yes. If you just randomly pick "a problem" you're only going to have a partial understanding of the problem and how people are currently solving it. To make a good solution you really need to understand the problem and the only way you're going to do that is by experiencing them yourself.

"AFNetworking was originally created by Scott Raymond and Mattt Thompson in the development of Gowalla for iPhone."

Agreed. Starting with a framework first unless you truly and deeply understand the space is going to either make something that kind of solves a problem but has its own problems, period, or kind of solves a problems but has its own problems for a really long time while you slowly refine it. And the odds of dedicating yourself to solving a problem that you don't have a need to solve are low.

Most are built to serve a need that the developer has. But, yes, there is also pain and struggle.

So, would building a framework to gain more experience be a bad idea?

I would say "yes": the interesting part of building a framework comes from taking a deep understanding of a problem domain and generalizing it so that others can take advantage of what you learned. As this is not what you will be doing, you won't actually be getting the associated "experience". That said, you will not be "wasting your time" (you can, after all, sort of simulate this experience with superficial knowledge), but there are probably numerous more direct things you could be doing.

Thank you saurik, I'll save the framework for one of these occasions. Any suggetion what a "more direct [thing]" could be to become a better developer? I'm currently working on privly (https://github.com/hery/privly-ios), reading iOS dev books, open-source code, and blogs.

I'd suggest: build more apps (or other software) that you want to see in the world, and make sure to finish some projects to your own satisfaction.