Use a concrete-then-abstract pattern to pull readers forward. Start with a concrete example, probably more concrete than you feel it needs to be, and then make the more general point.

Any rationale? I generally state the principle first and then give a concrete example.

If I do it the other way around, I fear the reader will go: "what's up with the story?" - and turn off.

That is pretty much what happens in reverse when other authors launch into examples without telling me where they are going with them.