My problem with "dog" and "animal" is not that I hate metaphors, but because the example tends to teach students that "X is a Y" is justification for "class X inherits from class Y". It's also usually found in books that focus more on the hammer than on the nails, if you know what I mean.
Recursive fib is usually taught to show how a naive translation of a recursive formula into code can cause poor performance. I can't think of a better example.
Reclusive FP is usssually the first example of the FP textbook, and is used to teach how elegant FP is from the beginnin jn spite of the fact that you should never write that (and who needs to write fib anyways). Inheritance is subtyping at the basic level: we all know a dog is an animal, and that all animals share a common ancestor. It is a crude instrument, especially in Java, and often can't be used, but not because the concept of extension is flawed in some ways. If you had traits/mixins, extension can be used much more widely.
I'm just as annoyed at the ideological "composition, not inheritance" crowd. The truth is, one has to learn a bunch of generalizations and then practice a lot to get it; good design is just hard to teach in a book.
Recursive fib is usually taught to show how a naive translation of a recursive formula into code can cause poor performance. I can't think of a better example.