A convenient example can become a misleading ambassador for a complicated subject.

A single clear example is memorable, quotable, and almost always simpler than the subject it stands for. Once it becomes the reference case, people reason from it, argue from it, and design around it, and all the complications it left out stop being part of the conversation.

If one example keeps getting used for a complicated topic, deliberately go and find a second and third that behave differently. Hold all three. The point is not to discard the useful illustration but to stop it from silently becoming the whole picture.