Because cats have nine lives! LOL...

I think it is partly because of a cat's tendency to be able to get into things that other household animals cannot and also because of the alliteration effect that it has (using 3 [k] sounds)

I know the first recorded time the phrase was used was in 16th century. The original phrase was "Care killed the cat", "care" in this case meant "sorrow". As for the "cats", do you know any cat which is not willing to stick its nose into something which none of cat's business? How often do they climb into impossible places, you would never think of? :)))

Why do we flog a dead horse and not other dead animals? Why is it only dogs that have their day? If we hold something else in the hand, is it still worth two in the bush? :)

Maybe the cat was the first what jumped in there?..