Why do they say cats have nine lives?

Because they have a mystical ability to escape death !

The number nine appears to have had a magical or mystical appeal to our ancestors.It's a neat number is three times three. They liked nine: nine muses, nine gods ( meaning all the gods :'Lars Porsena of Clusium, by the nine gods he swore' is a classical reference to the principal gods of the Romans, but they got the magic number from the Etruscans, who had but nine) and there are Celtic spells involving repeating words and actions nine times, and so on.

So the reference is to the cat having a magical number of lives (or one charmed one ).

Thanks Fred! Meow!