The example is actually wrong. Functions are contravariant on their input and covariant on their output.

The basic premise behind subtypes is that an object of a subtype can be used anywhere that an object of its supertype can be used. Just as an example, if you replace f1 : Animal -> Animal with f2 : Cat -> Thing, there might be some animals that aren't cats, so f2 can't replace f1 everywhere. This is the reason that functions are contravariant on their input.