But now you can't assume that Birds can Fly. You have to catch InvalidOperationException on every invocation. And what's special about Fly? What above other Bird methods, surely the same can be done to all of them? Now you can't assume anything about a Bird. So what good is the Bird abstraction then, if you can't make any assumptions about it?

This is breaking the Liskov Substitution Principle[1]. By saying that Penguin is a subclass of Bird, you're implying that I should be able to stick a Penguin into any code that expects a Bird, that code will just work, without it having to care about the particularity of that Bird actually being a Penguin.

[1] http://en.wikipedia.org/wiki/Liskov_substitution_principle

[edit: grammar]