An example would be helpful (ironically), but I think it's because you already have fluency in many abstract concepts (rooted in a lifetime of concrete application and examples), and in this situation the abstraction is usually much faster to work with, and you're annoyed because the example is effectively a long-winded explanation.

I'm not saying a mature mathematician is wrong to ask for an abstract definition first. For them, that might work well. But it's wrong to conclude from that experience that the abstraction is somehow more primary, or that it could exist in isolation. They've just forgotten the process that got them there.