The fur... and the fact that you cant really depend on a cat to save your life one day 
If a (short-haired, can't speak on behalf of long-haired ones )cat is let out regularly, the fur that will 'left' inside will be minimal. Cats are very clean animals, even with their fur, you know.
Not wanting to sound morbid or negative in any way, but for lonely people, having a cat around might prevent them from developing suicidal ideas so in that perspective it's saving their life. I'm not saying
you're lonely, but I'm talking in general. Besides that, I think the number of pets saving their master's life is very low, whatever type they may be.
