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Just because some things should not be represented as objects doesn't mean that nothing should.

And mammals and dogs as a concrete example- a metaphor, if you will- is an example of a powerful way to teach abstract ideas, not an indication that something is wrong.

What I would find enlightening is how the mammal-dog relationship fails, not how there is something out there for which the model may not fit.

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The problem with 'dog is a mammal' is that there's basically no obvious scenario in which you'd actually be modeling things this way unless you're trying to build some kind of ecosystem simulation or whatever. If you want to teach people, not only what inheritance is but why it's useful, you need to use a situation where inheritance makes things easier.

Here's an example that's visual: You are putting interaction widgets on the screen- they display some text, perhaps some other visual indicator, and have a button or text area or slider or something on them (there are some of each). Your base class has the setup: the window/panel/whatever-your-language-calls it, the place where the text goes, and the place where the variable widget goes. All of these widgets inherit the base class, and only differ in the user response portion. This makes it very easy to change the interaction style.

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