Another fundamental flaw in my opinion is the cats-and-dogs analogy frequently used to highlight the use of inheritance in OO.

Cats and dogs being mammals is a taxonomy. It's data, not code. Unfortunately, I see OO programmers coding taxonomies all the time just for the sake of it, ending up with deep inheritance trees of classes without ever taking the step back and asking themselves, why they do it the first place. (e.g. to share functionality or to reuse code)